A029282 Expansion of 1/((1-x^3)*(1-x^5)*(1-x^8)*(1-x^9)).

1, 0, 0, 1, 0, 1, 1, 0, 2, 2, 1, 2, 2, 2, 3, 3, 3, 4, 5, 4, 5, 6, 5, 7, 8, 7, 9, 10, 9, 11, 12, 11, 14, 15, 14, 17, 18, 17, 20, 21, 21, 24, 25, 25, 28, 30, 29, 32, 35, 34, 38, 40, 39, 44, 46, 45, 50, 52, 52, 57, 59, 59, 64, 67, 67, 72, 75, 75, 81, 84, 84, 90, 94

Offset

0,9

Comments

Number of partitions of n into parts 3, 5, 8, and 9. - 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 (0,0,1,0,1,0,0,0,1,0,-1,-1,-1,-1,0,1,0,0,0,1,0,1,0,0,-1).

Formula

a(n) = floor((2*n^3+75*n^2+1008*n+3328)/12960 - ((2*n^2+2*n) mod 3)*n/27 + ((4*n^3+n+1) mod 5)/5 + ((n+2) mod 3)*22/81). - Hoang Xuan Thanh, Mar 30 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^5)(1-x^8)(1-x^9)), {x, 0, 70}], x] (* Harvey P. Dale, Jun 07 2012 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^5)*(1-x^8)*(1-x^9)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A332086 A197081 A029395 * A333123 A289494 A393674

Adjacent sequences: A029279 A029280 A029281 * A029283 A029284 A029285

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved