A373015 Number of partitions p of n such that max(p) == 2 mod 3.

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

Links

Table of n, a(n) for n=0..50.

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

Cf. A000041, A363045, A373014.

Sequence in context: A035943 A240177 A035555 * A039875 A206555 A110539

Adjacent sequences: A373012 A373013 A373014 * A373016 A373017 A373018

Keyword

nonn

Author

Seiichi Manyama, May 20 2024

Status

approved