A029339 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^8)*(1-x^11)).

1, 0, 0, 0, 1, 1, 0, 0, 2, 1, 1, 1, 2, 2, 1, 2, 4, 2, 2, 3, 5, 4, 3, 4, 7, 5, 5, 6, 8, 7, 7, 8, 11, 9, 9, 11, 13, 12, 12, 13, 17, 15, 15, 17, 20, 19, 19, 20, 25, 23, 23, 25, 29, 28, 28, 30, 35, 33, 33, 36, 41, 39, 39, 42, 48, 46

Offset

0,9

Comments

Number of partitions of n into parts 4, 5, 8, and 11. - Hoang Xuan Thanh, Apr 22 2026

Links

Table of n, a(n) for n=0..65.

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

Formula

a(n) = floor((n+14)*(n^2+28*n-108)/10560 + (n mod 2)*n/64 + ((n^3+2*n^2+3*n+2) mod 4)*(n+12)/32 + ((2*n^3+4*n^2+3*n+2) mod 5)/5 + ((7*n^3+8*n^2+8*n+1) mod 11)/11). - Hoang Xuan Thanh, Apr 22 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^8)(1-x^11)), {x, 0, 80}], x] (* Harvey P. Dale, May 08 2019 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^5)*(1-x^8)*(1-x^11)) + O(x^80)) \\ Hoang Xuan Thanh, Apr 22 2026

Crossrefs

Sequence in context: A145704 A139632 A145705 * A029364 A122586 A079487

Adjacent sequences: A029336 A029337 A029338 * A029340 A029341 A029342

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved