A029029 - OEIS

A029029

Expansion of 1/((1-x)*(1-x^2)*(1-x^9)*(1-x^12)).

1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 8, 10, 11, 13, 14, 16, 17, 20, 21, 24, 26, 29, 31, 35, 37, 41, 44, 48, 51, 56, 59, 64, 68, 73, 77, 84, 88, 95, 100, 107, 112, 120, 125, 133, 140, 148, 155, 165, 172, 182, 190, 200, 208, 220, 228, 240, 250, 262, 272, 286, 296

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OFFSET

0,3

COMMENTS

Number of partitions of n into parts 1, 2, 9 and 12. - Ilya Gutkovskiy, May 14 2017

LINKS

Table of n, a(n) for n=0..61.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,0,0,0,1,-1,-1,2,-1,-1,1,0,0,0,0,0,-1,1,1,-1).

FORMULA

G.f.: 1/((1-x)(1-x^2)(1-x^9)(1-x^12)).

a(n) = floor((n^3+36*n^2+357*n+1520)/1296 + ((n+16)/108)*[(n mod 3)=0] + ((n+8)/48)*[(n mod 2)=0]). - Hoang Xuan Thanh, Jul 17 2025

MATHEMATICA

CoefficientList[Series[1/((1 - x) (1 - x^2) (1 - x^9) (1 - x^12)), {x, 0, 80}], x] (* Wesley Ivan Hurt, Feb 15 2017 *)

CROSSREFS

Sequence in context: A194210 A112672 A025765 * A025157 A006141 A185229

Adjacent sequences: A029026 A029027 A029028 * A029030 A029031 A029032

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(54) onwards from Hoang Xuan Thanh, Jul 17 2025

STATUS

approved