A025849 Expansion of 1/((1-x^3)*(1-x^7)*(1-x^12)).

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

Offset

0,13

Comments

Number of partitions of n into parts 3, 7, and 12. - Hoang Xuan Thanh, Sep 06 2025

Links

Table of n, a(n) for n=0..73.

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

Formula

a(n) = floor((n^2 + 36*n + 288)/504 - (n+4)*(n mod 3)/36 + ((3*(n^2 + n + 1)) mod 7)/7). - Hoang Xuan Thanh, Sep 06 2025

Prog

(PARI) a(n) = (n^2 + 36*n + 288 - 14*(n+4)*(n%3) + 72*((3*n^2+3*n+3)%7)) \504 \\ Hoang Xuan Thanh, Sep 06 2025

Crossrefs

Sequence in context: A371243 A378284 A025898 * A088782 A291984 A066672

Adjacent sequences: A025846 A025847 A025848 * A025850 A025851 A025852

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved