A025863 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^11)).

1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 12, 11, 11, 12, 13, 13, 13, 13, 14, 14, 15, 15, 15

Offset

0,16

Comments

Number of partitions of n into parts 4, 5, and 11. - 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,-1,0,1,0,0,0,-1,-1,0,0,0,1).

Formula

a(n) = floor((n^2+20*n)/440 + ((3*n^2+5*n+5) mod 11)/11 + ((3*n^2+3) mod 5)/5). - Hoang Xuan Thanh, Sep 09 2025

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^11)), {x, 0, 80}], x] (* Harvey P. Dale, Jun 14 2017 *)
(* Alternative: *)
LinearRecurrence[{0, 0, 0, 1, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2}, 80] (* Harvey P. Dale, Jun 14 2017 *)

Prog

(PARI) a(n) = (n^2+20*n+160 + 40*(((3*n^2+5*n+5)%11) + ((n+3)%5)-((n+1)%5)))\440 \\ Hoang Xuan Thanh, Sep 09 2025

Crossrefs

Sequence in context: A071784 A161638 A066030 * A346307 A339352 A372515

Adjacent sequences: A025860 A025861 A025862 * A025864 A025865 A025866

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved