A029102 Expansion of 1/((1-x)*(1-x^5)*(1-x^9)*(1-x^12)).

1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 23, 25, 26, 28, 30, 32, 34, 37, 39, 41, 44, 46, 49, 52, 54, 57, 61, 64, 67, 71, 74, 78, 82, 85, 89, 94, 98, 102, 107, 111, 116

Offset

0,6

Comments

Number of partitions of n into parts 1, 5, 9 and 12. - Michel Marcus, Jul 20 2025

Links

Table of n, a(n) for n=0..59.

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

Formula

a(n) = floor((2*n^3 + 81*n^2 + 948*n + 6745)/6480 + (n/108)*[(n mod 3)=0] - (1/5)*[(n mod 5)=3]). - Hoang Xuan Thanh, Jul 20 2025

Mathematica

CoefficientList[Series[1/((1-x)(1-x^5)(1-x^9)(1-x^12)), {x, 0, 70}], x] (* Jinyuan Wang, Mar 18 2020 *)

Crossrefs

Sequence in context: A029126 A269850 A036054 * A241086 A194818 A029081

Adjacent sequences: A029099 A029100 A029101 * A029103 A029104 A029105

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved