A029208 - OEIS

A029208

Expansion of 1/((1-x^2)*(1-x^5)*(1-x^9)*(1-x^10)).

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 3, 2, 3, 2, 4, 4, 4, 4, 5, 6, 8, 6, 8, 7, 10, 10, 10, 11, 12, 14, 16, 14, 17, 16, 20, 20, 21, 22, 24, 26, 29, 27, 31, 30, 35, 36, 37, 39, 41, 44, 48, 46, 51, 50, 57, 58, 60, 62, 65, 69, 74, 72

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,10

COMMENTS

Number of partitions of n into parts 2, 5, 9, and 10. - Hoang Xuan Thanh, Oct 16 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,-1,0,1,1,-1,-1,0,-1,-1,1,1,0,-1,0,1,0,0,1,0,-1).

FORMULA

a(n) = floor((n^3+39*n^2+414*n+3456)/5400 - n*(n mod 2)/40 + (n+9)*((4*n^2+4*n+2) mod 5)/50 + (1-(floor(n/3) mod 3))*((2*n^2+n) mod 3)/3). - Hoang Xuan Thanh, Oct 16 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^2)(1-x^5)(1-x^9)(1-x^10)), {x, 0, 70}], x] (* Harvey P. Dale, Jul 23 2013 *)

PROG

(PARI) Vec(1/((1-x^2)*(1-x^5)*(1-x^9)*(1-x^10)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

CROSSREFS

Sequence in context: A165005 A167530 A205789 * A322592 A329896 A366262

Adjacent sequences: A029205 A029206 A029207 * A029209 A029210 A029211

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved