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A373015
Number of partitions p of n such that max(p) == 2 mod 3.
1
0, 0, 1, 1, 2, 3, 4, 5, 8, 10, 14, 19, 25, 33, 45, 58, 76, 99, 127, 162, 209, 263, 333, 419, 524, 652, 813, 1003, 1239, 1524, 1868, 2281, 2786, 3382, 4104, 4965, 5993, 7213, 8676, 10396, 12447, 14866, 17725, 21087, 25063, 29711, 35185, 41589, 49089, 57839, 68079
OFFSET
0,5
FORMULA
G.f.: Sum_{k>=0} x^(3*k+2) / Product_{j=1..3*k+2} (1-x^j).
A000041(n) = A363045(n) + A373014(n) + a(n).
EXAMPLE
a(8) = 8 counts these partitions: 8, 53, 521, 5111, 2222, 22211, 221111, 2111111.
PROG
(PARI) my(N=60, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, N, x^(3*k+2)/prod(j=1, 3*k+2, 1-x^j))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 20 2024
STATUS
approved