A029319 Expansion of 1/((1-x^3)*(1-x^8)*(1-x^10)*(1-x^11)).

1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 3, 3, 3, 4, 3, 4, 4, 4, 5, 5, 5, 7, 6, 7, 8, 7, 8, 9, 8, 10, 10, 11, 12, 12, 13, 14, 13, 15, 15, 16, 17, 18, 19, 20, 20, 22, 22, 23, 24, 25, 26, 28, 28, 30, 31, 32, 33, 35

Offset

0,12

Comments

Number of partitions of n into parts 3, 8, 10, and 11. - Hoang Xuan Thanh, Apr 14 2026

Links

Table of n, a(n) for n=0..66.

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

Formula

a(n) = floor((n^3+48*n^2+744*n-5490)/15840 - (n mod 2)*(n+6)/160 + (2*((2*n^3+4*n^2+3*n+3) mod 8) + ((n+4) mod 8) - ((n+3) mod 8) - ((n^3+n^2+2*n) mod 4))/16 + ((n^3+4*n^2+7*n+10) mod 11)/11). - Hoang Xuan Thanh, Apr 14 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^8)(1-x^10)(1-x^11)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^8)*(1-x^10)*(1-x^11)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 14 2026

Crossrefs

Sequence in context: A217869 A116674 A025836 * A243987 A050205 A281530

Adjacent sequences: A029316 A029317 A029318 * A029320 A029321 A029322

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved