A029262 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^8)*(1-x^9)).

1, 0, 0, 1, 1, 0, 1, 1, 2, 2, 1, 2, 4, 2, 2, 4, 5, 4, 5, 5, 7, 7, 6, 7, 11, 9, 9, 12, 13, 12, 14, 14, 17, 18, 17, 19, 24, 21, 22, 26, 28, 27, 30, 31, 35, 36, 35, 38, 45, 42, 43, 49, 52, 51, 55, 56, 62, 64, 63, 67, 76, 73, 75

Offset

0,9

Comments

Number of partitions of n into parts 3, 4, 8, and 9. - Vincenzo Librandi, Jun 03 2014

Links

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

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

Formula

a(n) = floor((n^3+36*n^2+204*n+2592)/5184 - (n mod 2)*n/64 + ((2*n^2+1) mod 3)*n/27 + ((n^3+n^2+n+2) mod 4)*n/32 + ((n^2+n+2) mod 4)/4 - ((n^3+n^2+2*n) mod 4)/6). - Hoang Xuan Thanh, Mar 23 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^4) (1 - x^8) (1 - x^9)), {x, 0, 70}], x] (* Harvey P. Dale, Sep 18 2011 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^8)*(1-x^9)) + O(x^80)) \\ Jinyuan Wang, Mar 12 2020

Crossrefs

Sequence in context: A210531 A066954 A144925 * A392628 A363825 A368470

Adjacent sequences: A029259 A029260 A029261 * A029263 A029264 A029265

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved