A029225 Expansion of 1/((1-x^2)*(1-x^6)*(1-x^11)*(1-x^12)).

1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 1, 4, 1, 4, 1, 4, 2, 6, 2, 6, 2, 7, 4, 10, 4, 10, 4, 11, 6, 14, 6, 14, 7, 16, 10, 20, 10, 20, 11, 22, 14, 26, 14, 27, 16, 30, 20, 35, 20, 36, 22, 39, 26, 44, 27, 46, 30, 50, 35, 56, 36, 58, 39, 62

Offset

0,7

Comments

Number of partitions of n into parts 2, 6, 11, and 12. - 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 (0,1,0,0,0,1,0,-1,0,0,1,1,-1,-1,0,0,-1,-1,1,1,0,0,-1,0,1,0,0,0,1,0,-1).

Formula

From Wesley Ivan Hurt, May 24 2021: (Start)

G.f.: 1/((1-x^2)*(1-x^6)*(1-x^11)*(1-x^12)).

a(n) = a(n-2)+a(n-6)-a(n-8)+a(n-11)+a(n-12)-a(n-13)-a(n-14)-a(n-17)-a(n-18)+a(n-19)+a(n-20)-a(n-23)+a(n-25)+a(n-29)-a(n-31). (End)

a(n) = floor((n^3+63*n^2+1156*n+8640)/9504 - (n^2+31*n+145)*(n mod 2)/288 + n*(((n+5) mod 6)-((n+1) mod 6))/216 + ((9*n^3+6*n^2+9*n+1) mod 11)/11). - Hoang Xuan Thanh, Oct 24 2025

Mathematica

CoefficientList[Series[1/((1 - x^2) (1 - x^6) (1 - x^11) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 02 2014 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^6)*(1-x^11)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 15 2020

Crossrefs

Sequence in context: A096030 A025815 A219199 * A341977 A309937 A116127

Adjacent sequences: A029222 A029223 A029224 * A029226 A029227 A029228

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved