A029338 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^8)*(1-x^10)).

1, 0, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 3, 2, 4, 2, 6, 3, 4, 4, 7, 6, 6, 4, 10, 7, 10, 6, 11, 10, 12, 10, 14, 11, 16, 12, 20, 14, 18, 16, 23, 20, 22, 18, 29, 23, 30, 22, 32, 29, 34, 30, 38, 32, 42, 34, 48, 38, 46, 42

Offset

0,9

Comments

Number of partitions of n into parts 4, 5, 8, and 10. - Hoang Xuan Thanh, Apr 22 2026

Links

Table of n, a(n) for n=0..63.

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

Formula

a(n) = floor((n^3+48*n^2+356*n+1920)/9600 - (n mod 2)*(n^2+27*n)/640 + ((n^2+3*n+2) mod 4)*n/64 + ((n^2+2*n+2) mod 5)*n/50 + ((n^3+2*n^2+3*n+4) mod 5)/5). - Hoang Xuan Thanh, Apr 22 2026

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^8)(1-x^10)), {x, 0, 70}], x] (* Harvey P. Dale, Nov 01 2011 *)
(* Alternative: *)
LinearRecurrence[{0, 0, 0, 1, 1, 0, 0, 1, -1, 1, 0, -1, -1, -1, -1, 0, 1, -1, 1, 0, 0, 1, 1, 0, 0, 0, -1}, {1, 0, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 3, 2, 4, 2, 6, 3, 4, 4, 7, 6, 6}, 70] (* Harvey P. Dale, Apr 16 2016 *)

Prog

(PARI) Vec(1/((1-x^4)*(1-x^5)*(1-x^8)*(1-x^10)) + O(x^90)) \\ Hoang Xuan Thanh, Apr 22 2026

Crossrefs

Sequence in context: A334956 A335881 A239703 * A240883 A048272 A112329

Adjacent sequences: A029335 A029336 A029337 * A029339 A029340 A029341

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved