A029241 Expansion of 1/((1-x^2)*(1-x^9)*(1-x^10)*(1-x^11)).

1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 5, 4, 6, 4, 6, 4, 6, 5, 7, 7, 9, 9, 10, 10, 10, 10, 11, 11, 13, 13, 16, 15, 18, 16, 19, 17, 20, 19, 22, 22, 25, 25, 27, 27, 29, 29, 31, 31, 34, 34, 38, 37, 41, 40, 44

Offset

0,11

Comments

Number of partitions of n into parts 2, 9, 10, and 11. - 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, 0, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, -1).

Formula

G.f.: 1/((1-x^2)*(1-x^9)*(1-x^10)*(1-x^11)).

a(n) = a(n-2) + a(n-9) + a(n-10) - a(n-12) - a(n-13) - a(n-19) - a(n-20) + a(n-22) + a(n-23) + a(n-30) - a(n-32). - Wesley Ivan Hurt, Feb 12 2026

a(n) = floor((n^3+48*n^2+840*n+4248)/11880 - (n mod 2)*(n+16)/40 + (((n+7) mod 10) + ((n+6) mod 10) + ((n+5) mod 10) + ((n+4) mod 10) - 2*((n+1) mod 10) - 2*(n mod 10))/50 + ((5*n^3+9*n^2+9*n+10) mod 11)/11). - Hoang Xuan Thanh, Jun 18 2026

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^9) (1 - x^10) (1 - x^11)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^9)*(1-x^10)*(1-x^11)) + O(x^80)) \\ Jinyuan Wang, Mar 12 2020

Crossrefs

Sequence in context: A061798 A345206 A318585 * A226749 A277090 A103376

Adjacent sequences: A029238 A029239 A029240 * A029242 A029243 A029244

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved