A029271 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^11)*(1-x^12)).

1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 3, 1, 2, 4, 3, 2, 4, 4, 4, 4, 5, 6, 7, 5, 7, 9, 8, 7, 10, 10, 10, 11, 12, 13, 15, 13, 15, 18, 17, 16, 20, 20, 21, 22, 23, 25, 28, 25, 28, 32, 31, 30, 35, 36, 37, 38, 40, 43, 46, 43, 47, 52, 51, 50, 57, 58, 59, 61, 64, 67, 71

Offset

0,12

Comments

Number of partitions of n into parts 3, 4, 11, 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 (0,0,1,1,0,0,-1,0,0,0,1,1,0,-1,-2,-1,0,1,1,0,0,0,-1,0,0,1,1,0,0,-1).

Formula

a(n) = floor((n^3+45*n^2+366*n+2016)/9504 - (n mod 2)*n/96 + ((2*n^2+1) mod 3)*(n+12)/36 + ((n^3+2*n+1) mod 4)*n/48 + ((9*n^3+9*n^2+5*n+5) mod 11)/11). - Hoang Xuan Thanh, Mar 27 2026

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^4) (1 - x^11) (1 - x^12)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)
LinearRecurrence[{0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 1, 1, 0, -1, -2, -1, 0, 1, 1, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, -1}, {1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 3, 1, 2, 4, 3, 2, 4, 4, 4, 4, 5, 6, 7, 5, 7, 9, 8, 7}, 70] (* Harvey P. Dale, Jul 29 2021 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^11)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 12 2020

Crossrefs

Sequence in context: A177993 A256990 A071503 * A035459 A048232 A163256

Adjacent sequences: A029268 A029269 A029270 * A029272 A029273 A029274

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved