Munafo's Classical Sequences

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3, 11, 47, 239, 1439, 10079, 80639, 725759, 7257599, 79833599, 958003199, 12454041599, 174356582399, ...

MCS124048 : A₀ = 1; A_K+1 = K A_K + A_K + K (score: 4)

3, 11, 48, 252, 1561, 11180, 91002, 830199, 8392993, 93153123, 1126230470, 14734149234, 207404319747, ...

MCS868929 : A₀ = 0; A₁ = 0; A_K+1 = K A_K + A_K-1 + 1 (score: 5)

3, 11, 52, 301, 2055, 16139, 143196, 1415821, 15430835, 183754199, 2373373752, 33043478329, 493278801183, ...

MCS1710605 : A₀ = -1; A₁ = -1; A_K+1 = K A_K - A_K-1 (score: 5)

3, 12, 27, 48, 75, 108, 147, 192, 243, 300, 363, 432, 507, 588, 675, 768, 867, 972, 1083, 1200, 1323, 1452, 1587, 1728, 1875, 2028, 2187, 2352, 2523, 2700, 2883, 3072, 3267, 3468, 3675, 3888, ...

MCS1763 : A_K = 3 K² (score: 4)

3, 12, 33, 72, 135, 228, 357, 528, 747, 1020, 1353, 1752, 2223, 2772, 3405, 4128, 4947, 5868, 6897, 8040, 9303, 10692, 12213, 13872, 15675, 17628, 19737, 22008, 24447, 27060, 29853, 32832, 36003, ...

MCS7060 : A_K = K³ + 2 K (score: 5)

3, 12, 33, 78, 171, 360, 741, 1506, 3039, 6108, 12249, 24534, 49107, 98256, 196557, 393162, 786375, 1572804, 3145665, 6291390, 12582843, 25165752, 50331573, 100663218, 201326511, 402653100, ...

MCS3883 : A₀ = 0; A_K+1 = 2 A_K + 3 K (score: 5)

3, 12, 39, 120, 363, 1092, 3279, 9840, 29523, 88572, 265719, 797160, 2391483, 7174452, 21523359, 64570080, 193710243, 581130732, 1743392199, 5230176600, 15690529803, 47071589412, 141214768239, ...

MCS1979 : A₀ = 0; A_N = 3 A_N-1 + 3 (score: 6)

Weighing problem numbers (3^N-3)/2

3, 12, 40, 105, 231, 448, 792, 1305, 2035, 3036, 4368, 6097, 8295, 11040, 14416, 18513, 23427, 29260, 36120, 44121, 53383, 64032, 76200, 90025, 105651, 123228, 142912, 164865, 189255, 216256, ...

MCS15648 : A₀ = 0; A_K+1 = A_K + K³ + 1 (score: 5)

3, 12, 45, 192, 975, 5868, 41097, 328800, 2959227, 29592300, 325515333, 3906184032, 50780392455, 710925494412, ...

MCS1934 (alias MCS61904) : A₀ = 0; A_K+1 = K A_K + 3 K (score: 5)

3, 12, 60, 360, 2520, 20160, 181440, 1814400, 19958400, 239500800, 3113510400, 43589145600, 653837184000, ...

MCS62352 : A₀ = 1; A_K+1 = K A_K + 3 A_K (score: 5)

3, 13, 34, 70, 125, 203, 308, 444, 615, 825, 1078, 1378, 1729, 2135, 2600, 3128, 3723, 4389, 5130, 5950, 6853, 7843, 8924, 10100, 11375, 12753, 14238, 15834, 17545, 19375, 21328, 23408, 25619, ...

MCS31010 : A₀ = 0; A_K+1 = A_K + 2 K² + K (score: 5)

3, 13, 43, 111, 241, 463, 813, 1333, 2071, 3081, 4423, 6163, 8373, 11131, 14521, 18633, 23563, 29413, 36291, 44311, 53593, 64263, 76453, 90301, 105951, 123553, 143263, 165243, 189661, 216691, ...

MCS124036 : A₀ = 1; A_K+1 = A_K + K³ + K (score: 5)

3, 13, 61, 321, 1951, 13693, 109593, 986401, 9864091, 108505101, 1302061333, 16926797473, 236975164791, ...

MCS123976 : A₀ = 1; A_K+1 = K A_K + A_K + K² (score: 5)

3, 13, 79, 633, 6331, 75973, 1063623, 17017969, 306323443, 6126468861, 134782314943, ...

MCS3906 (alias MCS62504, MCS125009) : A₀ = 0; A_K+1 = 2 K A_K + 1 (score: 4)

3, 13, 81, 661, 6691, 80953, 1140033, 18321481, 330926691, 6636855301, 146341743313, ...

MCS1708678 : A₀ = 1; A₁ = 1; A_K+1 = 2 K A_K + A_K-1 (score: 5)

3, 15, 42, 90, 165, 273, 420, 612, 855, 1155, 1518, 1950, 2457, 3045, 3720, 4488, 5355, 6327, 7410, 8610, 9933, 11385, 12972, 14700, 16575, 18603, 20790, 23142, 25665, 28365, 31248, 34320, 37587, ...

MCS7747 : A₀ = 0; A_K+1 = A_K + 3 K² (score: 5)

3, 15, 105, 945, 10395, 135135, 2027025, 34459425, 654729075, 13749310575, 316234143225, ...

MCS61992 (alias MCS124497) : A₀ = 1; A_K+1 = 2 K A_K + A_K (score: 4)

Odd semifactorials (A001147)

3, 17, 55, 129, 251, 433, 687, 1025, 1459, 2001, 2663, 3457, 4395, 5489, 6751, 8193, 9827, 11665, 13719, 16001, 18523, 21297, 24335, 27649, 31251, 35153, 39367, 43905, 48779, 54001, 59583, 65537, ...

MCS14146 : A_K = 2 K³ + 1 (score: 5)

3, 17, 133, 1313, 15623, 217409, 3462921, 62115169, 1238840459, 27192374929, 651378157837, ...

MCS1710726 : A₀ = 1; A₁ = 1; A_K+1 = 2 K A_K - A_K-1 (score: 5)

3, 18, 57, 132, 255, 438, 693, 1032, 1467, 2010, 2673, 3468, 4407, 5502, 6765, 8208, 9843, 11682, 13737, 16020, 18543, 21318, 24357, 27672, 31275, 35178, 39393, 43932, 48807, 54030, 59613, 65568, ...

MCS14114 : A_K = 2 K³ + K (score: 5)

3, 19, 73, 201, 451, 883, 1569, 2593, 4051, 6051, 8713, 12169, 16563, 22051, 28801, 36993, 46819, 58483, 72201, 88201, 106723, 128019, 152353, 180001, 211251, 246403, 285769, 329673, 378451, ...

MCS61962 : A₀ = 1; A_K+1 = A_K + 2 K³ (score: 5)

3, 24, 81, 192, 375, 648, 1029, 1536, 2187, 3000, 3993, 5184, 6591, 8232, 10125, 12288, 14739, 17496, 20577, 24000, 27783, 31944, 36501, 41472, 46875, 52728, 59049, 65856, 73167, 81000, 89373, ...

MCS3523 : A_K = 3 K³ (score: 5)

4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

MCS123147 (alias MCS123275) : A₀ = 4; A_K+1 = K A_K (score: 5)

4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, 0, 1, 4, ...

MCS98370 : A₀ = 0; A₁ = 1; A₂ = 4; A_N = A_N-3 (score: 5)

4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, ...

MCS3933 (alias MCS106755) : A₀ = 0; A_N = - A_N-1 + 4 (score: 5)

Horadam sequence W_n(0, 4; 1, 0)

4, 0, 16, 0, 64, 0, 256, 0, 1024, 0, 4096, 0, 16384, 0, 65536, 0, 262144, 0, 1048576, 0, 4194304, 0, 16777216, 0, 67108864, 0, 268435456, 0, 1073741824, 0, 4294967296, 0, 17179869184, 0, ...

MCS3339 : A₀ = 0; A₁ = 1; A_N = 4 A_N-2 (score: 5)

Horadam sequence W_n(0, 1; 4, 0)

4, 0, 24, 0, 192, 0, 1920, 0, 23040, 0, 322560, 0, 5160960, 0, 92897280, 0, 1857945600, 0, 40874803200, 0, 980995276800, 0, ...

MCS26704 : A₀ = 0; A₁ = 1; A_K+1 = K A_K-1 + 2 A_K-1 (score: 5)

4, 0, 32, 0, 384, 0, 6144, 0, 122880, 0, 2949120, 0, 82575360, 0, 2642411520, 0, 95126814720, 0, ...

MCS13314 : A₀ = 0; A₁ = 1; A_K+1 = 2 K A_K-1 (score: 4)

4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, ...

MCS3147862 : A₀ = 1; A₁ = 1; A₂ = 4; A_N = A_N-3 (score: 5)

4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, ...

MCS427018 : A₀ = 1; A₁ = 4; A_N = A_N-2 (score: 4)

Horadam sequence W_n(1, 4; 1, 0)

4, 1, 8, 3, 32, 15, 192, 105, 1536, 945, 15360, 10395, 184320, 135135, 2580480, 2027025, 41287680, 34459425, 743178240, 654729075, 14863564800, 13749310575, 326998425600, 316234143225, ...

MCS426058 : A₀ = 1; A₁ = 4; A_K+1 = K A_K-1 (score: 5)

4, 2, 5, 3, 6, 4, 7, 5, 8, 6, 9, 7, 10, 8, 11, 9, 12, 10, 13, 11, 14, 12, 15, 13, 16, 14, 17, 15, 18, 16, 19, 17, 20, 18, 21, 19, 22, 20, 23, 21, 24, 22, 25, 23, 26, 24, 27, 25, 28, 26, 29, 27, ...

MCS1737738 : A₀ = 1; A₁ = 4; A_N = A_N-2 + 1 (score: 5)

4, 2, 6, 5, 10, 10, 16, 17, 24, 26, 34, 37, 46, 50, 60, 65, 76, 82, 94, 101, 114, 122, 136, 145, 160, 170, 186, 197, 214, 226, 244, 257, 276, 290, 310, 325, 346, 362, 384, 401, 424, 442, 466, 485, ...

MCS1713162 : A₀ = 1; A₁ = 4; A_K+1 = A_K-1 + K (score: 5)

4, 2, 8, 4, 16, 8, 32, 16, 64, 32, 128, 64, 256, 128, 512, 256, 1024, 512, 2048, 1024, 4096, 2048, 8192, 4096, 16384, 8192, 32768, 16384, 65536, 32768, 131072, 65536, 262144, 131072, 524288, ...

MCS854538 : A₀ = 1; A₁ = 4; A_N = 2 A_N-2 (score: 5)

Horadam sequence W_n(1, 4; 2, 0)

4, 3, 7, 6, 10, 9, 13, 12, 16, 15, 19, 18, 22, 21, 25, 24, 28, 27, 31, 30, 34, 33, 37, 36, 40, 39, 43, 42, 46, 45, 49, 48, 52, 51, 55, 54, 58, 57, 61, 60, 64, 63, 67, 66, 70, 69, 73, 72, 76, 75, ...

MCS250736 : A₀ = 1; A_K+1 = - A_K + 3 K + 1 (score: 5)

4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, 4, 1, 4, ...

MCS3147882 : A₀ = 1; A₁ = 4; A₂ = 4; A_N = A_N-3 (score: 5)

4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, ...

MCS1771 (alias MCS123915, MCS3416171) : A_N = 4 (score: 4)

Horadam sequence W_n(4, 4; 0, 1) ; Horadam sequence W_n(4, 4; 1, 0)

4, 4, 5, 7, 10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 109, 124, 140, 157, 175, 194, 214, 235, 257, 280, 304, 329, 355, 382, 410, 439, 469, 500, 532, 565, 599, 634, 670, 707, 745, 784, 824, 865, ...

MCS496139 : A₀ = 4; A_K+1 = A_K + K (score: 5)

4, 4, 7, 7, 10, 10, 13, 13, 16, 16, 19, 19, 22, 22, 25, 25, 28, 28, 31, 31, 34, 34, 37, 37, 40, 40, 43, 43, 46, 46, 49, 49, 52, 52, 55, 55, 58, 58, 61, 61, 64, 64, 67, 67, 70, 70, 73, 73, 76, 76, ...

MCS1761798 : A₀ = 1; A₁ = 1; A_N = A_N-2 + 3 (score: 5)

4, 4, 8, 8, 12, 12, 16, 16, 20, 20, 24, 24, 28, 28, 32, 32, 36, 36, 40, 40, 44, 44, 48, 48, 52, 52, 56, 56, 60, 60, 64, 64, 68, 68, 72, 72, 76, 76, 80, 80, 84, 84, 88, 88, 92, 92, 96, 96, 100, ...

MCS7787 : A₀ = 0; A_K+1 = - A_K + 4 K (score: 5)

4, 4, 10, 10, 22, 22, 46, 46, 94, 94, 190, 190, 382, 382, 766, 766, 1534, 1534, 3070, 3070, 6142, 6142, 12286, 12286, 24574, 24574, 49150, 49150, 98302, 98302, 196606, 196606, 393214, 393214, ...

MCS3491078 : A₀ = 1; A₁ = 1; A_N = 2 A_N-2 + 2 (score: 5)

4, 4, 13, 13, 40, 40, 121, 121, 364, 364, 1093, 1093, 3280, 3280, 9841, 9841, 29524, 29524, 88573, 88573, 265720, 265720, 797161, 797161, 2391484, 2391484, 7174453, 7174453, 21523360, 21523360, ...

MCS3395 (alias MCS434625, MCS1738502) : A₀ = 0; A₁ = 1; A_N = 3 A_N-2 + 1 (score: 5)

4, 4, 16, 16, 64, 64, 256, 256, 1024, 1024, 4096, 4096, 16384, 16384, 65536, 65536, 262144, 262144, 1048576, 1048576, 4194304, 4194304, 16777216, 16777216, 67108864, 67108864, 268435456, ...

MCS1709830 : A₀ = 1; A₁ = 1; A_N = 4 A_N-2 (score: 5)

Horadam sequence W_n(1, 1; 4, 0)

4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, 5, 1, 4, ...

MCS786954 : A₀ = 1; A₁ = 4; A₂ = 5; A_N = A_N-3 (score: 5)

4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, ...

MCS854027 : A₀ = 4; A₁ = 5; A_N = A_N-2 (score: 5)

Horadam sequence W_n(4, 5; 1, 0)

4, 5, 4, 5, 8, 9, 8, 9, 12, 13, 12, 13, 16, 17, 16, 17, 20, 21, 20, 21, 24, 25, 24, 25, 28, 29, 28, 29, 32, 33, 32, 33, 36, 37, 36, 37, 40, 41, 40, 41, 44, 45, 44, 45, 48, 49, 48, 49, 52, 53, 52, ...

MCS6859798 : A₀ = 1; A₁ = 0; A_K+1 = - A_K-1 + 2 K (score: 5)

4N and 4N+1, repeated

4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, ...

MCS7086 (alias MCS500747) : A_K = K + 4 (score: 5)

4, 5, 6, 10, 12, 14, 19, 22, 25, 31, 35, 39, 46, 51, 56, 64, 70, 76, 85, 92, 99, 109, 117, 125, 136, 145, 154, 166, 176, 186, 199, 210, 221, 235, 247, 259, 274, 287, 300, 316, 330, 344, 361, 376, ...

MCS26281014 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = A_K-2 + K + 1 (score: 5)

4, 5, 6, 13, 16, 19, 34, 41, 48, 79, 94, 109, 172, 203, 234, 361, 424, 487, 742, 869, 996, 1507, 1762, 2017, 3040, 3551, 4062, 6109, 7132, 8155, 12250, 14297, 16344, 24535, 28630, 32725, 49108, ...

MCS12716598 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = 2 A_K-2 + K (score: 5)

4, 5, 7, 6, 7, 7, 10, 11, 13, 12, 13, 13, 16, 17, 19, 18, 19, 19, 22, 23, 25, 24, 25, 25, 28, 29, 31, 30, 31, 31, 34, 35, 37, 36, 37, 37, 40, 41, 43, 42, 43, 43, 46, 47, 49, 48, 49, 49, 52, 53, ...

MCS398385 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = - A_K-2 + 2 K (score: 5)

4, 5, 9, 11, 16, 19, 25, 29, 36, 41, 49, 55, 64, 71, 81, 89, 100, 109, 121, 131, 144, 155, 169, 181, 196, 209, 225, 239, 256, 271, 289, 305, 324, 341, 361, 379, 400, 419, 441, 461, 484, 505, 529, ...

MCS856581 (alias MCS6984198) : A₀ = 0; A₁ = -1; A_K+1 = A_K-1 + K (score: 4)

Interleaves N² with N+(N+1)² (A000290 and A028387)

4, 5, 9, 14, 20, 30, 42, 59, 82, 112, 153, 207, 279, 375, 502, 671, 895, 1192, 1586, 2108, 2800, 3717, 4932, 6542, 8675, 11501, 15245, 20205, 26776, 35481, 47013, 62290, 82528, 109338, 144854, ...

MCS25461814 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = A_K-1 + A_K-2 + K (score: 5)

4, 5, 9, 14, 23, 37, 60, 97, 157, 254, 411, 665, 1076, 1741, 2817, 4558, 7375, 11933, 19308, 31241, 50549, 81790, 132339, 214129, 346468, 560597, 907065, 1467662, 2374727, 3842389, 6217116, ...

MCS1721354 : A₀ = 1; A₁ = 4; A_N = A_N-1 + A_N-2 (score: 5)

Horadam sequence W_n(1, 4; 1, 1)

4, 5, 11, 14, 22, 27, 37, 44, 56, 65, 79, 90, 106, 119, 137, 152, 172, 189, 211, 230, 254, 275, 301, 324, 352, 377, 407, 434, 466, 495, 529, 560, 596, 629, 667, 702, 742, 779, 821, 860, 904, 945, ...

MCS62225 : A₀ = -1; A_K+1 = - A_K + K² (score: 4)

4, 5, 12, 15, 30, 37, 68, 83, 146, 177, 304, 367, 622, 749, 1260, 1515, 2538, 3049, 5096, 6119, 10214, 12261, 20452, 24547, 40930, 49121, 81888, 98271, 163806, 196573, 327644, 393179, 655322, ...

MCS3346 (alias MCS6956294) : A₀ = 0; A₁ = 1; A_K+1 = 2 A_K-1 + K (score: 4)

4, 5, 15, 19, 50, 63, 157, 197, 480, 601, 1451, 1815, 4366, 5459, 13113, 16393, 39356, 49197, 118087, 147611, 354282, 442855, 1062869, 1328589, 3188632, 3985793, 9565923, 11957407, 28697798, ...

MCS1713926 : A₀ = 1; A₁ = 1; A_K+1 = 3 A_K-1 + K (score: 5)

4, 5, 21, 31, 148, 249, 1333, 2491, 14664, 29893, 190633, 418503, 2859496, 6696049, 48611433, 120528883, 923617228, 2410577661, 19395961789, 53032708543, 446107121148, ...

MCS217097 (alias MCS54304) : A₀ = 0; A₁ = 0; A_K+1 = K A_K-1 + 1 (score: 4)

4, 6, 6, 5, 5, 7, 10, 12, 12, 11, 11, 13, 16, 18, 18, 17, 17, 19, 22, 24, 24, 23, 23, 25, 28, 30, 30, 29, 29, 31, 34, 36, 36, 35, 35, 37, 40, 42, 42, 41, 41, 43, 46, 48, 48, 47, 47, 49, 52, 54, ...

MCS6891021 : A₀ = -1; A₁ = -1; A_K+1 = A_K - A_K-1 + K (score: 5)

4, 6, 7, 6, 6, 7, 10, 12, 13, 12, 12, 13, 16, 18, 19, 18, 18, 19, 22, 24, 25, 24, 24, 25, 28, 30, 31, 30, 30, 31, 34, 36, 37, 36, 36, 37, 40, 42, 43, 42, 42, 43, 46, 48, 49, 48, 48, 49, 52, 54, ...

MCS796769 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = - A_K-2 + 2 K (score: 5)

4, 6, 8, 6, 6, 6, 10, 12, 14, 12, 12, 12, 16, 18, 20, 18, 18, 18, 22, 24, 26, 24, 24, 24, 28, 30, 32, 30, 30, 30, 34, 36, 38, 36, 36, 36, 40, 42, 44, 42, 42, 42, 46, 48, 50, 48, 48, 48, 52, 54, ...

MCS3187085 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = - A_K-2 + 2 K (score: 5)

4, 6, 8, 14, 18, 22, 30, 36, 42, 52, 60, 68, 80, 90, 100, 114, 126, 138, 154, 168, 182, 200, 216, 232, 252, 270, 288, 310, 330, 350, 374, 396, 418, 444, 468, 492, 520, 546, 572, 602, 630, 658, ...

MCS3186957 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = A_K-2 + 2 K (score: 5)

4, 6, 9, 14, 18, 23, 30, 36, 43, 52, 60, 69, 80, 90, 101, 114, 126, 139, 154, 168, 183, 200, 216, 233, 252, 270, 289, 310, 330, 351, 374, 396, 419, 444, 468, 493, 520, 546, 573, 602, 630, 659, ...

MCS796737 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = A_K-2 + 2 K (score: 5)

4, 6, 11, 15, 22, 28, 37, 45, 56, 66, 79, 91, 106, 120, 137, 153, 172, 190, 211, 231, 254, 276, 301, 325, 352, 378, 407, 435, 466, 496, 529, 561, 596, 630, 667, 703, 742, 780, 821, 861, 904, 946, ...

MCS7832 (alias MCS6858, MCS6957574) : A₀ = 0; A_K+1 = - A_K + K² + 1 (score: 4)

4, 6, 14, 20, 38, 52, 90, 120, 198, 260, 418, 544, 862, 1116, 1754, 2264, 3542, 4564, 7122, 9168, 14286, 18380, 28618, 36808, 57286, 73668, 114626, 147392, 229310, 294844, 458682, 589752, 917430, ...

MCS3429638 : A₀ = 1; A₁ = 1; A_K+1 = 2 A_K-1 + 2 K (score: 5)

4, 6, 20, 35, 126, 252, 1016, 2277, 10170, 25058, 122052, 325767, 1708742, 4886520, 27339888, 83070857, 492118002, 1578346302, 9842360060, 33145272363, 216531921342, 762341264372, ...

MCS13376 : A₀ = 0; A₁ = 1; A_K+1 = K A_K-1 + K (score: 4)

4, 7, 9, 14, 19, 23, 30, 37, 43, 52, 61, 69, 80, 91, 101, 114, 127, 139, 154, 169, 183, 200, 217, 233, 252, 271, 289, 310, 331, 351, 374, 397, 419, 444, 469, 493, 520, 547, 573, 602, 631, 659, ...

MCS398369 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = A_K-2 + 2 K (score: 5)

4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, ...

MCS3539 (alias MCS14171, MCS63296) : A_K = 3 K + 1 (score: 4)

4, 7, 12, 17, 24, 31, 40, 49, 60, 71, 84, 97, 112, 127, 144, 161, 180, 199, 220, 241, 264, 287, 312, 337, 364, 391, 420, 449, 480, 511, 544, 577, 612, 647, 684, 721, 760, 799, 840, 881, 924, 967, ...

MCS857345 : A₀ = -1; A₁ = 0; A_K+1 = A_K-1 + 2 K (score: 5)

4, 7, 13, 19, 28, 37, 49, 61, 76, 91, 109, 127, 148, 169, 193, 217, 244, 271, 301, 331, 364, 397, 433, 469, 508, 547, 589, 631, 676, 721, 769, 817, 868, 919, 973, 1027, 1084, 1141, 1201, 1261, ...

MCS1718790 : A₀ = 1; A₁ = 1; A_K+1 = A_K-1 + 3 K (score: 5)

4, 7, 13, 22, 37, 61, 100, 163, 265, 430, 697, 1129, 1828, 2959, 4789, 7750, 12541, 20293, 32836, 53131, 85969, 139102, 225073, 364177, 589252, 953431, 1542685, 2496118, 4038805, 6534925, ...

MCS6988294 : A₀ = 1; A₁ = 1; A_N = A_N-1 + A_N-2 + 2 (score: 5)

4, 7, 16, 31, 64, 127, 256, 511, 1024, 2047, 4096, 8191, 16384, 32767, 65536, 131071, 262144, 524287, 1048576, 2097151, 4194304, 8388607, 16777216, 33554431, 67108864, 134217727, 268435456, ...

MCS6964486 : A₀ = 1; A₁ = 1; A_N = A_N-1 + 2 A_N-2 + 1 (score: 5)

4, 7, 19, 40, 97, 217, 508, 1159, 2683, 6160, 14209, 32689, 75316, 173383, 399331, 919480, 2117473, 4875913, 11228332, 25856071, 59541067, 137109280, 315732481, 727060321, 1674257764, 3855438727, ...

MCS3363 (alias MCS1722118) : A₀ = 0; A₁ = 1; A_N = A_N-1 + 3 A_N-2 (score: 5)

Horadam sequence W_n(0, 1; 3, 1) ; Horadam sequence W_n(1, 1; 3, 1)

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, ...

MCS3531 (alias MCS1966) : A_K = 4 K (score: 4)

4, 8, 12, 17, 24, 32, 40, 49, 60, 72, 84, 97, 112, 128, 144, 161, 180, 200, 220, 241, 264, 288, 312, 337, 364, 392, 420, 449, 480, 512, 544, 577, 612, 648, 684, 721, 760, 800, 840, 881, 924, 968, ...

MCS213793 : A₀ = 0; A₁ = 0; A_K+1 = - A_K-1 + K² (score: 4)

4, 8, 13, 19, 26, 34, 43, 53, 64, 76, 89, 103, 118, 134, 151, 169, 188, 208, 229, 251, 274, 298, 323, 349, 376, 404, 433, 463, 494, 526, 559, 593, 628, 664, 701, 739, 778, 818, 859, 901, 944, 988, ...

MCS253216 (alias MCS502337) : A₀ = 1; A_K+1 = A_K + K + 3 (score: 5)

4, 8, 13, 22, 36, 56, 86, 131, 197, 294, 437, 647, 955, 1407, 2070, 3042, 4467, 6556, 9618, 14106, 20684, 30325, 44455, 65164, 95515, 139997, 205189, 300733, 440760, 645980, 946745, 1387538, ...

MCS25756726 : A₀ = 1; A₁ = 1; A₂ = 1; A_K+1 = A_K + A_K-2 + K (score: 5)

4, 8, 15, 21, 28, 34, 43, 53, 66, 78, 91, 103, 118, 134, 153, 171, 190, 208, 229, 251, 276, 300, 325, 349, 376, 404, 435, 465, 496, 526, 559, 593, 630, 666, 703, 739, 778, 818, 861, 903, 946, 988, ...

MCS196913 : A₀ = 0; A₁ = 1; A₂ = 1; A_K+1 = - A_K-2 + K² (score: 5)

4, 8, 16, 29, 51, 87, 146, 242, 398, 651, 1061, 1725, 2800, 4540, 7356, 11913, 19287, 31219, 50526, 81766, 132314, 214103, 346441, 560569, 907036, 1467632, 2374696, 3842357, 6217083, 10059471, ...

MCS13931014 : A₀ = 1; A₁ = 1; A_K+1 = A_K + A_K-1 + K + 1 (score: 5)

4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, ...

MCS248331 : A₀ = 4; A_N = 2 A_N-1 (score: 5)

Horadam sequence W_n(4, 4; 0, 2)

4, 8, 19, 32, 54, 80, 117, 160, 216, 280, 359, 448, 554, 672, 809, 960, 1132, 1320, 1531, 1760, 2014, 2288, 2589, 2912, 3264, 3640, 4047, 4480, 4946, 5440, 5969, 6528, 7124, 7752, 8419, 9120, ...

MCS13704 : A₀ = 0; A₁ = 1; A_K+1 = A_K-1 + K² - 1 (score: 5)

4, 8, 19, 39, 82, 166, 337, 677, 1360, 2724, 5455, 10915, 21838, 43682, 87373, 174753, 349516, 699040, 1398091, 2796191, 5592394, 11184798, 22369609, 44739229, 89478472, 178956956, 357913927, ...

MCS6890758 : A₀ = 1; A₁ = 1; A_K+1 = A_K + 2 A_K-1 + K (score: 5)

4, 8, 28, 76, 272, 880, 3328, 12128, 48736, 194272, 827840, 3547648, 15965248, 72727616, 344136832, 1653233920, 8191833728, 41256512128, 213285020416, ...

MCS53792 (alias MCS3440790) : A₀ = 0; A₁ = 1; A_K+1 = A_K + K A_K-1 + A_K-1 (score: 5)

4, 9, 12, 16, 24, 33, 40, 48, 60, 73, 84, 96, 112, 129, 144, 160, 180, 201, 220, 240, 264, 289, 312, 336, 364, 393, 420, 448, 480, 513, 544, 576, 612, 649, 684, 720, 760, 801, 840, 880, 924, 969, ...

MCS3420694 : A₀ = 1; A₁ = 0; A_K+1 = - A_K-1 + K² (score: 5)

4, 9, 13, 17, 24, 33, 41, 49, 60, 73, 85, 97, 112, 129, 145, 161, 180, 201, 221, 241, 264, 289, 313, 337, 364, 393, 421, 449, 480, 513, 545, 577, 612, 649, 685, 721, 760, 801, 841, 881, 924, 969, ...

MCS3476614 : A₀ = 1; A₁ = 1; A_K+1 = - A_K-1 + K² + 1 (score: 5)

4, 9, 15, 21, 27, 34, 43, 54, 66, 78, 90, 103, 118, 135, 153, 171, 189, 208, 229, 252, 276, 300, 324, 349, 376, 405, 435, 465, 495, 526, 559, 594, 630, 666, 702, 739, 778, 819, 861, 903, 945, 988, ...

MCS393825 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = - A_K-2 + K² (score: 5)

4, 9, 16, 21, 27, 33, 43, 54, 67, 78, 90, 102, 118, 135, 154, 171, 189, 207, 229, 252, 277, 300, 324, 348, 376, 405, 436, 465, 495, 525, 559, 594, 631, 666, 702, 738, 778, 819, 862, 903, 945, 987, ...

MCS1575309 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = - A_K-2 + K² (score: 5)

4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, ...

MCS440 (alias MCS7826, MCS14154, MCS28310, MCS252496)

A_K = K² (score: 2)

Perfect squares : N×N (A000290)

4, 9, 16, 29, 45, 65, 93, 126, 165, 214, 270, 334, 410, 495, 590, 699, 819, 951, 1099, 1260, 1435, 1628, 1836, 2060, 2304, 2565, 2844, 3145, 3465, 3805, 4169, 4554, 4961, 5394, 5850, 6330, 6838, ...

MCS1575181 : A₀ = 0; A₁ = 0; A₂ = 0; A_K+1 = A_K-2 + K² (score: 5)

4, 9, 17, 29, 45, 66, 93, 126, 166, 214, 270, 335, 410, 495, 591, 699, 819, 952, 1099, 1260, 1436, 1628, 1836, 2061, 2304, 2565, 2845, 3145, 3465, 3806, 4169, 4554, 4962, 5394, 5850, 6331, 6838, ...

MCS393793 : A₀ = 0; A₁ = 0; A₂ = 1; A_K+1 = A_K-2 + K² (score: 5)

4, 9, 18, 33, 58, 99, 166, 275, 452, 739, 1204, 1957, 3176, 5149, 8342, 13509, 21870, 35399, 57290, 92711, 150024, 242759, 392808, 635593, 1028428, 1664049, 2692506, 4356585, 7049122, 11405739, ...

MCS3445253 : A₀ = 0; A₁ = -1; A_K+1 = A_K + A_K-1 + K (score: 5)

4, 9, 18, 35, 68, 133, 262, 519, 1032, 2057, 4106, 8203, 16396, 32781, 65550, 131087, 262160, 524305, 1048594, 2097171, 4194324, 8388629, 16777238, 33554455, 67108888, 134217753, 268435482, ...

MCS502448 : A₀ = 1; A_K+1 = 2 A_K - K + 2 (score: 5)

4, 9, 19, 33, 54, 81, 117, 161, 216, 281, 359, 449, 554, 673, 809, 961, 1132, 1321, 1531, 1761, 2014, 2289, 2589, 2913, 3264, 3641, 4047, 4481, 4946, 5441, 5969, 6529, 7124, 7753, 8419, 9121, ...

MCS3508358 : A₀ = 1; A₁ = 1; A_K+1 = A_K-1 + K² - 1 (score: 5)

4, 9, 19, 36, 65, 113, 192, 321, 531, 872, 1425, 2321, 3772, 6121, 9923, 16076, 26033, 42145, 68216, 110401, 178659, 289104, 467809, 756961, 1224820, 1981833, 3206707, 5188596, 8395361, 13584017, ...

MCS6892038 : A₀ = 1; A₁ = 1; A_K+1 = A_K + A_K-1 + 2 K (score: 5)

4, 9, 20, 34, 56, 83, 120, 164, 220, 285, 364, 454, 560, 679, 816, 968, 1140, 1329, 1540, 1770, 2024, 2299, 2600, 2924, 3276, 3653, 4060, 4494, 4960, 5455, 5984, 6544, 7140, 7769, 8436, 9138, ...

MCS427073 : A₀ = -1; A₁ = 0; A_K+1 = A_K-1 + K² (score: 5)

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