A029377 Expansion of 1/((1-x^4)*(1-x^10)*(1-x^11)*(1-x^12)).

1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 3, 1, 3, 2, 4, 1, 3, 2, 4, 1, 4, 3, 6, 3, 6, 4, 7, 3, 6, 4, 8, 4, 8, 6, 11, 6, 10, 7, 12, 6, 11, 8, 14, 8, 14, 11, 17, 10, 16, 12, 19, 11, 18, 14, 22, 14, 22, 17, 25, 16, 25

Offset

0,13

Comments

Number of partitions of n into parts 4, 10, 11, and 12. - Hoang Xuan Thanh, Jun 22 2026

Links

Table of n, a(n) for n=0..70.

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

Formula

a(n) = floor((n^3+72*n^2+1212*n+8776)/31680 - (n mod 2)*(n^2+37*n+400)/960 + ((n^2+n+2) mod 4)*n/96 + (((n+3) mod 4) + 2*((n+2) mod 4) - 3*((n+1) mod 4))/32 + ((6*n^3+3*n^2+n+10) mod 11)/11). - Hoang Xuan Thanh, Jun 22 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^10)(1-x^11)(1-x^12)), {x, 0, 70}], x] (* Harvey P. Dale, Mar 16 2016 *)
(* Alternative: *)
LinearRecurrence[{0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 3, 1, 3, 2, 4, 1, 3, 2, 4, 1, 4, 3, 6, 3, 6, 4, 7}, 80] (* Harvey P. Dale, Mar 16 2016 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^10)*(1-x^11)*(1-x^12)) + O(x^80)) \\ Hoang Xuan Thanh, Jun 22 2026

Crossrefs

Sequence in context: A265262 A124763 A029372 * A128186 A048823 A173655

Adjacent sequences: A029374 A029375 A029376 * A029378 A029379 A029380

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved