A029375 Expansion of 1/((1-x^4)*(1-x^9)*(1-x^10)*(1-x^12)).

1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 2, 1, 1, 0, 2, 1, 2, 1, 3, 2, 3, 1, 4, 2, 3, 2, 5, 3, 5, 3, 6, 4, 6, 3, 8, 5, 7, 5, 10, 6, 9, 6, 11, 8, 11, 7, 14, 10, 13, 9, 16, 11, 16, 11, 18, 14, 19, 13, 22, 16, 21, 16, 25, 18, 25, 19, 28, 22

Offset

0,13

Comments

Number of partitions of n into parts 4, 9, 10, and 12. - Hoang Xuan Thanh, Jun 22 2026

Links

Table of n, a(n) for n=0..69.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,0,0,0,1,1,0,1,-1,-1,0,-1,0,0,-1,0,-1,-1,1,0,1,1,0,0,0,0,1,0,0,0,-1).

Formula

a(n) = floor((n^3+66*n^2+1116*n+15800)/25920 - (n mod 2)*(n^2+35*n+381)/960 - ((2*n^2+n) mod 3)*n/108 + ((n^2+3*n+2) mod 4)*(n+19)/96). - Hoang Xuan Thanh, Jun 22 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^9)(1-x^10)(1-x^12)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^9)*(1-x^10)*(1-x^12)) + O(x^80)) \\ Hoang Xuan Thanh, Jun 22 2026

Crossrefs

Sequence in context: A341973 A143792 A230121 * A071462 A101979 A369241

Adjacent sequences: A029372 A029373 A029374 * A029376 A029377 A029378

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved