A373012
Number of distinct partitions p of n such that max(p) == 1 mod 3.
Original entry on oeis.org
0, 1, 0, 0, 1, 1, 1, 3, 2, 2, 4, 3, 4, 7, 7, 8, 12, 13, 15, 20, 21, 24, 31, 34, 39, 49, 54, 62, 76, 84, 97, 116, 130, 148, 174, 195, 221, 257, 287, 325, 374, 419, 472, 540, 604, 679, 772, 861, 966, 1092, 1218, 1362, 1533, 1706, 1903, 2133, 2368, 2635, 2943, 3263, 3622, 4033, 4463
Offset: 0
a(7) = 3 counts these partitions: 7, 43, 421.
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my(N=70, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, x^(3*k+1)*prod(j=1, 3*k, 1+x^j))))
A373013
Number of distinct partitions p of n such that max(p) == 2 mod 3.
Original entry on oeis.org
0, 0, 1, 1, 0, 1, 1, 1, 3, 3, 3, 5, 5, 5, 8, 9, 9, 13, 15, 17, 23, 26, 29, 36, 41, 46, 57, 64, 72, 87, 98, 111, 131, 149, 168, 197, 223, 251, 291, 328, 369, 423, 476, 534, 609, 683, 765, 867, 970, 1084, 1222, 1365, 1522, 1710, 1905, 2121, 2374, 2639, 2931, 3269, 3627, 4020, 4471, 4950
Offset: 0
a(8) = 3 counts these partitions: 8, 53, 521.
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my(N=70, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, N, x^(3*k+2)*prod(j=1, 3*k+1, 1+x^j))))
A373029
Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) is the number of distinct partitions p of n such that max(p) is a multiple of k.
Original entry on oeis.org
1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 1, 0, 3, 1, 1, 1, 1, 0, 4, 2, 2, 1, 1, 1, 0, 5, 3, 1, 2, 1, 1, 1, 0, 6, 3, 1, 2, 2, 1, 1, 1, 0, 8, 4, 3, 2, 2, 2, 1, 1, 1, 0, 10, 5, 3, 2, 3, 2, 2, 1, 1, 1, 0, 12, 6, 4, 2, 3, 3, 2, 2, 1, 1, 1, 0, 15, 7, 6, 3, 3, 4, 3, 2, 2, 1, 1, 1, 0, 18, 9, 6, 4, 3, 4, 4, 3, 2, 2, 1, 1, 1
Offset: 0
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 2, 1, 1;
0, 2, 1, 1, 1;
0, 3, 1, 1, 1, 1;
0, 4, 2, 2, 1, 1, 1;
0, 5, 3, 1, 2, 1, 1, 1;
0, 6, 3, 1, 2, 2, 1, 1, 1;
0, 8, 4, 3, 2, 2, 2, 1, 1, 1;
0, 10, 5, 3, 2, 3, 2, 2, 1, 1, 1;
0, 12, 6, 4, 2, 3, 3, 2, 2, 1, 1, 1;
0, 15, 7, 6, 3, 3, 4, 3, 2, 2, 1, 1, 1;
0, 18, 9, 6, 4, 3, 4, 4, 3, 2, 2, 1, 1, 1;
Showing 1-3 of 3 results.