A373014 Number of partitions p of n such that max(p) == 1 mod 3.

0, 1, 1, 1, 2, 2, 3, 5, 7, 9, 14, 18, 25, 34, 45, 58, 78, 99, 128, 165, 210, 264, 336, 419, 525, 655, 813, 1003, 1242, 1522, 1867, 2283, 2783, 3379, 4105, 4960, 5989, 7214, 8670, 10391, 12447, 14858, 17719, 21088, 25055, 29705, 35187, 41581, 49084, 57844, 68072, 79974

Offset

0,5

Links

Table of n, a(n) for n=0..51.

Formula

G.f.: Sum_{k>=0} x^(3*k+1) / Product_{j=1..3*k+1} (1-x^j).

A000041(n) = A363045(n) + a(n) + A373015(n).

Example

a(7) = 5 counts these partitions: 7, 43, 421, 4111, 1111111.

Prog

(PARI) my(N=60, x='x+O('x^N)); concat(0, Vec(sum(k=0, N, x^(3*k+1)/prod(j=1, 3*k+1, 1-x^j))))

Crossrefs

Cf. A000041, A363045, A373015.

Cf. A027193.

Sequence in context: A369570 A190660 A180158 * A320689 A173693 A058278

Adjacent sequences: A373011 A373012 A373013 * A373015 A373016 A373017

Keyword

nonn

Author

Seiichi Manyama, May 20 2024

Status

approved