A025858 Expansion of 1/((1-x^3)*(1-x^11)*(1-x^12)).

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

Offset

0,13

Comments

Number of partitions of n into parts 3, 11, and 12. - Hoang Xuan Thanh, Sep 09 2025

Links

Table of n, a(n) for n=0..78.

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

Formula

a(n) = floor((n^2 + 4*n + 124)/792 + (n+7)*((n+2) mod 3)/36 + (((n+1)*(5-2*n)) mod 11)/11). - Hoang Xuan Thanh, Sep 09 2025

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^11)(1-x^12)), {x, 0, 100}], x] (* or *) LinearRecurrence[ {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2, 3, 1}, 100] (* Harvey P. Dale, Jul 01 2022 *)

Prog

(PARI) a(n) = (n^2+4*n+124 + 22*(n+7)*((n+2)%3) + 72*(((n+1)*(5-2*n))%11))\792 \\ Hoang Xuan Thanh, Sep 09 2025

Crossrefs

Sequence in context: A010872 A220663 A220659 * A237451 A215592 A025684

Adjacent sequences: A025855 A025856 A025857 * A025859 A025860 A025861

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved