A029232 Expansion of 1/((1-x^2)*(1-x^7)*(1-x^9)*(1-x^12)).

1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 3, 5, 5, 5, 6, 6, 7, 7, 8, 9, 8, 11, 9, 12, 11, 13, 13, 15, 15, 16, 17, 18, 18, 21, 20, 23, 23, 25, 25, 28, 28, 30, 31, 33, 33, 37, 36, 40, 40, 43, 43, 47, 47, 50, 52, 54, 55, 59, 59, 63, 64, 68, 68, 74, 73

Offset

0,10

Comments

Number of partitions of n into parts 2, 7, 9, and 12. - 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 (0,1,0,0,0,0,1,0,0,0,-1,1,0,-1,0,-1,0,1,-1,0,0,0,1,0,0,0,0,1,0,-1).

Formula

a(n) = floor((n^3+45*n^2+672*n-1888)/9072 - (n mod 2)*n/48 + ((2*n^2+1) mod 3)*n/108 + ((6*n^3+4*n^2+5) mod 7)/7 + ((n^3+3*n^2+8*n+6) mod 9)/9 + (((n+7) mod 9) - ((n+6) mod 9) + 2*((n+5) mod 9) - 2*((n+4) mod 9))/27). - Hoang Xuan Thanh, Jun 13 2026

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^7) (1 - x^9) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^7)*(1-x^9)*(1-x^12)) + O(x^80)) \\ Hoang Xuan Thanh, Jun 13 2026

Crossrefs

Sequence in context: A035460 A261679 A147657 * A221531 A282970 A025807

Adjacent sequences: A029229 A029230 A029231 * A029233 A029234 A029235

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved