A025855 Expansion of 1/((1-x^3)*(1-x^9)*(1-x^11)).

1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 2, 3, 1, 2, 3, 1, 2, 4, 1, 3, 4, 2, 3, 5, 2, 3, 6, 2, 4, 6, 3, 4, 7, 3, 5, 8, 3, 6, 8, 4, 6, 9, 4, 7, 10, 5, 8, 10, 6, 8, 11, 6, 9, 12, 7, 10, 13, 8, 10, 14, 8, 11, 15, 9, 12, 16

Offset

0,10

Comments

Number of partitions of n into parts 3, 9, and 11. - Hoang Xuan Thanh, Sep 08 2025

Links

Table of n, a(n) for n=0..75.

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

Formula

G.f.: 1/((1-x^3)*(1-x^9)*(1-x^11)).

a(n) = a(n-3) + a(n-9) + a(n-11) - a(n-12) - a(n-14) - a(n-20) + a(n-23). - Wesley Ivan Hurt, Jan 20 2024

a(n) = floor((n^2 + n + 22*(n+8)*((n+2) mod 3) + 54*((n^2+n+5) mod 11))/594). - Hoang Xuan Thanh, Sep 08 2025

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^9)(1-x^11)), {x, 0, 80}], x] (* or *) LinearRecurrence[ {0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 1, 2, 0, 1, 3, 0, 2, 3, 1}, 80] (* Harvey P. Dale, Nov 07 2022 *)

Prog

(PARI) a(n) = (n^2+n+22*(n+8)*((n+2)%3)+54*((n^2+n+5)%11))\594 \\ Hoang Xuan Thanh, Sep 08 2025

Crossrefs

Sequence in context: A025678 A073189 A194519 * A394020 A215590 A097203

Adjacent sequences: A025852 A025853 A025854 * A025856 A025857 A025858

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved