A029372 Expansion of 1/((1-x^4)*(1-x^8)*(1-x^10)*(1-x^11)).

1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 1, 2, 0, 1, 1, 3, 0, 2, 2, 4, 1, 3, 2, 5, 1, 4, 3, 6, 2, 6, 4, 8, 3, 7, 5, 9, 4, 9, 6, 12, 6, 11, 8, 14, 7, 13, 9, 17, 9, 16, 12, 20, 11, 19, 14, 23, 13, 22, 17, 27, 16, 26, 20, 31, 19, 30, 23, 35

Offset

0,9

Comments

Number of partitions of n into parts 4, 8, 10, and 11. - Hoang Xuan Thanh, Jun 21 2026

Links

Table of n, a(n) for n=0..68.

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

Formula

a(n) = floor((n^3+66*n^2+956*n+3540)/21120 - (n mod 2)*(n^2+33*n+337)/640 + ((n^2+n+2) mod 4)*(n+16)/64 + ((9*n^3+2*n+4) mod 11)/11). - Hoang Xuan Thanh, Jun 21 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^8)(1-x^10)(1-x^11)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^8)*(1-x^10)*(1-x^11)) + O(x^80)) \\ Hoang Xuan Thanh, Jun 21 2026

Crossrefs

Sequence in context: A336469 A265262 A124763 * A029377 A128186 A048823

Adjacent sequences: A029369 A029370 A029371 * A029373 A029374 A029375

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved