A025922 Expansion of 1/((1-x^8)*(1-x^11)*(1-x^12)).

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 2, 0, 0, 1, 1, 0, 1, 1, 2, 1, 1, 2, 2, 0, 1, 1, 2, 1, 1, 2, 3, 1, 2, 2, 3, 1, 1, 2, 3, 1, 2, 3, 4, 2, 2, 3, 4, 1, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 2, 3, 4, 5, 3, 4, 5

Offset

0,25

Comments

Number of partitions of n into parts 8, 11, and 12. - Hoang Xuan Thanh, Sep 28 2025

Links

Table of n, a(n) for n=0..79.

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

Formula

a(n)= +a(n-8) +a(n-11) +a(n-12) -a(n-19) -a(n-20) -a(n-23) +a(n-31). - R. J. Mathar, Jul 19 2014

a(n) = floor((n^2-2*n-255 + 22*(n+23)*((n+3) mod 4))/2112 + ((2*n^2+7*n+7) mod 11)/11). - Hoang Xuan Thanh, Sep 28 2025

Mathematica

CoefficientList[Series[1/((1-x^8)(1-x^11)(1-x^12)), {x, 0, 120}], x] (* Harvey P. Dale, Aug 18 2019 *)
(* Alternative: *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 2, 0, 0, 1, 1, 0, 1}, 120] (* Harvey P. Dale, Aug 18 2019 *)

Prog

(PARI) a(n) = ((n^2-2*n-255 + 22*(n+23)*((n+3)%4))/2112 + ((2*n^2+7*n+7)%11)/11)\1 \\ Hoang Xuan Thanh, Sep 28 2025

Crossrefs

Sequence in context: A125203 A023565 A321925 * A342322 A161369 A151843

Adjacent sequences: A025919 A025920 A025921 * A025923 A025924 A025925

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved