A025857 - OEIS

A025857

Expansion of 1/((1-x^3)*(1-x^10)*(1-x^12)).

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

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OFFSET

0,13

COMMENTS

Number of partitions of n into parts 3, 10, and 12. - Hoang Xuan Thanh, Sep 09 2025

LINKS

Table of n, a(n) for n=0..76.

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

FORMULA

a(n) = floor((n^2 + 3*n*(15+(-1)^n) + 720)/720 - (n+12)*(n mod 3)/36). - Hoang Xuan Thanh, Sep 09 2025

MATHEMATICA

CoefficientList[Series[1/((1-x^3)(1-x^10)(1-x^12)), {x, 0, 80}], x] (* Harvey P. Dale, May 26 2011 *)

LinearRecurrence[{0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, -1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 1, 2, 2, 1, 3}, 80] (* Harvey P. Dale, Jun 29 2021 *)

PROG

(PARI) a(n) = (n^2 + 3*n*(15+(-1)^n) + 720 - 20*(n+12)*(n%3))\720 \\ Hoang Xuan Thanh, Sep 09 2025

CROSSREFS

Sequence in context: A025664 A025854 A190766 * A391911 A127788 A025656

Adjacent sequences: A025854 A025855 A025856 * A025858 A025859 A025860

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved