A029191 Expansion of 1/((1-x^2)*(1-x^4)*(1-x^10)*(1-x^11)).

1, 0, 1, 0, 2, 0, 2, 0, 3, 0, 4, 1, 5, 1, 6, 2, 7, 2, 8, 3, 10, 4, 12, 5, 14, 6, 16, 7, 18, 8, 21, 10, 24, 12, 27, 14, 30, 16, 33, 18, 37, 21, 41, 24, 46, 27, 50, 30, 55, 33, 60, 37, 66, 41, 72, 46, 78, 50, 84, 55, 91, 60, 98

Offset

0,5

Comments

a(n) is the number of partitions of n into parts 2, 4, 10, and 11. - Hoang Xuan Thanh, Oct 13 2025

Links

Table of n, a(n) for n=0..62.

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

Formula

a(n) = floor((n^3+57*n^2+932*n+3936)/5280 - (n^2+27*n+93)*(n mod 2)/160 + ((3*n^3+6*n^2+2*n+5) mod 11)/11). - Hoang Xuan Thanh, Oct 13 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^10)(1-x^11)), {x, 0, 70}], x] (* Harvey P. Dale, Jun 18 2013 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^4)*(1-x^10)*(1-x^11)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

Crossrefs

Sequence in context: A035457 A005868 A035455 * A094098 A326844 A261079

Adjacent sequences: A029188 A029189 A029190 * A029192 A029193 A029194

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved