A029325 Expansion of 1/((1-x^3)*(1-x^10)*(1-x^11)*(1-x^12)).

1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 3, 3, 3, 4, 3, 3, 4, 3, 3, 5, 4, 5, 7, 6, 6, 8, 6, 6, 8, 7, 7, 10, 9, 10, 12, 11, 11, 13, 11, 12, 14, 13, 14, 17, 16, 17, 19, 18, 18, 21, 19, 20, 23, 22, 23, 27, 25, 26

Offset

0,13

Comments

Number of partitions of n into parts 3, 10, 11, and 12. - Hoang Xuan Thanh, Apr 16 2026

Links

Table of n, a(n) for n=0..68.

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

Formula

a(n) = floor((n^3+54*n^2+708*n+4272)/23760 - (n mod 2)*n/240 + ((2*n^2+1) mod 3)*(5*n+29)/180 - (n mod 3)*5/54 + ((8*n^3+3*n^2+10*n+10) mod 11)/11). - Hoang Xuan Thanh, Apr 16 2026

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^10)(1-x^11)(1-x^12)), {x, 0, 70}], x] (* Harvey P. Dale, May 07 2011 *)

Prog

(PARI) Vec(1/((1-x^3)*(1-x^10)*(1-x^11)*(1-x^12)) + O(x^80)) \\ Jinyuan Wang, Mar 11 2020

Crossrefs

Sequence in context: A161070 A161109 A161044 * A276417 A025432 A025433

Adjacent sequences: A029322 A029323 A029324 * A029326 A029327 A029328

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved