A029301 Expansion of 1/((1-x^3)*(1-x^6)*(1-x^9)*(1-x^10)).

1, 0, 0, 1, 0, 0, 2, 0, 0, 3, 1, 0, 4, 1, 0, 5, 2, 0, 7, 3, 1, 8, 4, 1, 10, 5, 2, 12, 7, 3, 15, 8, 4, 17, 10, 5, 21, 12, 7, 24, 15, 8, 28, 17, 10, 32, 21, 12, 37, 24, 15, 41, 28, 17, 47, 32, 21, 52, 37, 24, 59, 41, 28, 65, 47, 32

Offset

0,7

Comments

Number of partitions of n into parts 3, 6, 9, and 10. - Hoang Xuan Thanh, Apr 08 2026

Links

Table of n, a(n) for n=0..65.

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

Formula

a(n) = floor((n^3+72*n^2+1512*n+5184)/9720 - (n mod 2)*n/120 - (n mod 3)*(n^2+28*n)/324 - ((2*n^2+2*n) mod 3)*n*5/162 + ((n^2+2) mod 3)/3). - Hoang Xuan Thanh, Apr 08 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^6)(1-x^9)(1-x^10)), {x, 0, 100}], x] (* Jinyuan Wang, Mar 11 2020 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^6)*(1-x^9)*(1-x^10)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 08 2026

Crossrefs

Sequence in context: A170980 A330369 A309577 * A263414 A162934 A392490

Adjacent sequences: A029298 A029299 A029300 * A029302 A029303 A029304

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved