A029253 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^9)).

1, 0, 0, 1, 1, 0, 2, 1, 1, 3, 2, 1, 5, 3, 2, 6, 5, 3, 9, 6, 5, 11, 9, 6, 15, 11, 9, 18, 15, 11, 23, 18, 15, 27, 23, 18, 34, 27, 23, 39, 34, 27, 47, 39, 34, 54, 47, 39, 64, 54, 47, 72, 64, 54, 84, 72, 64, 94, 84, 72, 108, 94, 84, 120, 108, 94, 136, 120, 108, 150

Offset

0,7

Comments

Number of partitions of n into parts 3, 4, 6, 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 (0,0,1,1,0,1,-1,0,0,-1,0,-1,0,0,-1,1,0,1,1,0,0,-1).

Formula

a(n) = floor((2*n^3 + 90*n^2 + 1215*n + 9110)/7776 + (n+16)*(-1)^n/96 - (n mod 3)*(n^2+22*n+162)/324 - ((2*n^2+2*n) mod 3)*n/81). - Hoang Xuan Thanh, Mar 17 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^4) (1 - x^6) (1 - x^9)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^9)) + O(x^80)) \\ Jinyuan Wang, Mar 12 2020

Crossrefs

Sequence in context: A355147 A049998 A288165 * A343196 A016441 A340581

Adjacent sequences: A029250 A029251 A029252 * A029254 A029255 A029256

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved