A029189 Expansion of 1/((1-x^2)*(1-x^4)*(1-x^9)*(1-x^11)).

1, 0, 1, 0, 2, 0, 2, 0, 3, 1, 3, 2, 4, 3, 4, 4, 5, 5, 6, 6, 8, 7, 10, 8, 12, 9, 14, 11, 16, 13, 18, 16, 20, 19, 22, 22, 25, 25, 28, 28, 32, 31, 36, 34, 41, 38, 45, 42, 50, 47, 54, 52, 59, 58, 64, 64, 70, 70, 76, 76, 83, 82

Offset

0,5

Comments

a(n) is the number of partitions of n into parts 2, 4, 9, and 11. - Hoang Xuan Thanh, Oct 12 2025

Links

Table of n, a(n) for n=0..61.

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

Formula

a(n) = floor((n^3+39*n^2+600*n+3600)/4752 - (n+11)*(n mod 2)/16 + ((7*n^3+9*n^2+9*n+10) mod 11)/11) - [(n mod 11)=3] + [(n mod 11)=4]. - Hoang Xuan Thanh, Oct 12 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^9)(1-x^11)), {x, 0, 80}], x] (* Harvey P. Dale, Nov 26 2014 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^4)*(1-x^9)*(1-x^11)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

Crossrefs

Sequence in context: A029190 A166865 A300575 * A035432 A029224 A029188

Adjacent sequences: A029186 A029187 A029188 * A029190 A029191 A029192

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved