A029210 - OEIS

A029210

Expansion of 1/((1-x^2)*(1-x^5)*(1-x^9)*(1-x^12)).

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 2, 4, 3, 4, 4, 5, 5, 6, 6, 7, 7, 9, 8, 10, 10, 11, 12, 13, 13, 15, 15, 17, 17, 20, 19, 22, 22, 24, 25, 27, 27, 30, 31, 33, 34, 37, 37, 41, 41, 44, 45, 49, 49, 53, 54, 57, 59, 63, 63, 68

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OFFSET

0,10

COMMENTS

Number of partitions of n into parts 2, 5, 9, and 12. - Hoang Xuan Thanh, Oct 18 2025

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = floor((n^3+42*n^2+552*n+3784)/6480 - n*(n mod 2)/48 + n*((n^2+n+1) mod 3)/108 + ((4*n^3+3*n^2+3*n+1) mod 5)/5 + [(n mod 9)=0]/3). - Hoang Xuan Thanh, Oct 18 2025

MATHEMATICA

CoefficientList[Series[1/((1 - x^2) (1 - x^5) (1 - x^9) (1 - x^12)), {x, 0, 70}], x] (* Vincenzo Librandi, Jun 02 2014 *)

PROG

(PARI) Vec(1/((1-x^2)*(1-x^5)*(1-x^9)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

CROSSREFS

Sequence in context: A014085 A248891 A171239 * A321909 A346598 A035433

Adjacent sequences: A029207 A029208 A029209 * A029211 A029212 A029213

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved