A029286 Expansion of 1/((1-x^3)*(1-x^5)*(1-x^9)*(1-x^10)).

1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 2, 2, 2, 4, 2, 2, 5, 4, 5, 5, 4, 6, 7, 7, 6, 8, 9, 9, 12, 9, 10, 14, 12, 14, 15, 14, 17, 19, 19, 18, 21, 22, 22, 27, 24, 25, 31, 29, 32, 33, 32, 36, 39, 40, 39, 43, 45, 46, 52, 48, 50, 58, 56

Offset

0,10

Comments

Number of partitions of n into parts 3, 5, 9, and 10. - Vincenzo Librandi, Jun 04 2014

Links

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

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

Formula

a(n) = floor((2*n^3+81*n^2+462*n+9720)/16200 + ((2*n^2+1) mod 3)*n/27 + ((n^2+2*n+2) mod 5)*(n+10)/50 - (n mod 3)/6). - Hoang Xuan Thanh, Mar 31 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^5) (1 - x^9) (1 - x^10)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 04 2014 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^5)*(1-x^9)*(1-x^10)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A333123 A289494 A393674 * A286221 A321347 A324383

Adjacent sequences: A029283 A029284 A029285 * A029287 A029288 A029289

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved