A029231 Expansion of 1/((1-x^2)*(1-x^7)*(1-x^9)*(1-x^11)).

1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 1, 3, 1, 3, 2, 3, 3, 3, 5, 3, 6, 4, 7, 5, 7, 7, 7, 9, 8, 11, 9, 12, 11, 13, 13, 14, 16, 15, 18, 17, 20, 19, 22, 22, 24, 25, 26, 28, 28, 31, 31, 34, 34, 37, 38, 40, 42, 43, 46, 46, 50, 50, 54, 55

Offset

0,10

Comments

Number of partitions of n into parts 2, 7, 9, and 11. - Vincenzo Librandi, Jun 02 2014

Links

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

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

Formula

a(n) = (2*n^3+87*n^2+1134*n-13184)/16632 - (n mod 2)/8 + ((n+2) mod 3)*10/27 + ((4*n^3+6*n^2+1) mod 7)/7 + (-2*((n+7) mod 9) +5*((n+6) mod 9) -6*((n+5) mod 9) +5*((n+4) mod 9) -2*((n+3) mod 9))/27 + (((4*n^3+9*n^2+2*n+10) mod 11) -((n+4) mod 11) +2*((n+3) mod 11) -((n+2) mod 11))/11. - Hoang Xuan Thanh, May 31 2026

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^7) (1 - x^9) (1 - x^11)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 02 2014 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^7)*(1-x^9)*(1-x^11)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020
(PARI) a(n) = (2*n^3+87*n^2+1134*n-19624)/16632 + [0, -1][n%2+1]/8 + [1, 4, 1, 2, 3, 0, 3][n%7+1]/7 + [28, 8, 36, 1, 35, 0, 28, 8, 18][n%9+1]/27 + [11, 4, 6, 8, 1, 9, 1, 12, 0, 11, 3][n%11+1]/11 \\ Hoang Xuan Thanh, May 31 2026

Crossrefs

Sequence in context: A025812 A263001 A109698 * A025808 A144079 A326839

Adjacent sequences: A029228 A029229 A029230 * A029232 A029233 A029234

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved