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A373013
Number of distinct partitions p of n such that max(p) == 2 mod 3.
2
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
0,9
FORMULA
G.f.: Sum_{k>=0} x^(3*k+2) * Product_{j=1..3*k+1} (1+x^j).
A000009(n) = A372893(n) + A373012(n) + a(n).
EXAMPLE
a(8) = 3 counts these partitions: 8, 53, 521.
PROG
(PARI) 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))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 20 2024
STATUS
approved