A025862 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^10)).

1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 2, 1, 1, 2, 2, 4, 1, 2, 2, 4, 4, 2, 2, 4, 4, 6, 2, 4, 4, 6, 6, 4, 4, 6, 6, 9, 4, 6, 6, 9, 9, 6, 6, 9, 9, 12, 6, 9, 9, 12, 12, 9, 9, 12, 12, 16, 9, 12, 12, 16, 16, 12, 12, 16, 16, 20, 12, 16

Offset

0,11

Comments

Number of partitions of n into parts 4, 5, and 10. - Hoang Xuan Thanh, Sep 09 2025

Links

Table of n, a(n) for n=0..72.

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

Formula

a(n) = floor((n^2 + 3*n + 272 + 5*n*(-1)^n + 8*(n+4)*((n+4) mod 5))/400). \\ Hoang Xuan Thanh, Sep 09 2025

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^10)), {x, 0, 80}], x] (* Harvey P. Dale, Mar 11 2023 *)
(* Alternative: *)
LinearRecurrence[ {0, 0, 0, 1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 2, 1, 1, 2}, 80] (* Harvey P. Dale, Mar 11 2023 *)

Prog

(PARI) a(n) = (n^2 + 3*n + 272 + 5*n*(-1)^n + 8*(n+4)*((n+4)%5))\400 \\ Hoang Xuan Thanh, Sep 09 2025

Crossrefs

Sequence in context: A290885 A059881 A096568 * A004540 A353945 A379071

Adjacent sequences: A025859 A025860 A025861 * A025863 A025864 A025865

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved