A025834 Expansion of 1/((1-x^3)*(1-x^4)*(1-x^12)).

1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 3, 1, 3, 3, 3, 3, 3, 3, 6, 3, 3, 6, 6, 3, 6, 6, 6, 6, 6, 6, 10, 6, 6, 10, 10, 6, 10, 10, 10, 10, 10, 10, 15, 10, 10, 15, 15, 10, 15, 15, 15, 15, 15, 15, 21, 15, 15, 21, 21, 15, 21

Offset

0,13

Comments

Number of partitions of n into parts 3, 4, and 12. - Hoang Xuan Thanh, Aug 26 2025

Links

Table of n, a(n) for n=0..66.

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

Formula

a(n) = floor((n^2 + 4*n + 8*(n+6)*(1-(n mod 3)) + 6*(n+10)*(1+((n+3) mod 4)))/288). - Hoang Xuan Thanh, Aug 26 2025

Prog

(PARI) a(n) = (n^2 + 4*n + 8*(n+6)*(1-n%3) + 6*(n+10)*(1+(n+3)%4))\288 \\ Hoang Xuan Thanh, Aug 26 2025

Crossrefs

Sequence in context: A091442 A392413 A379473 * A257379 A336456 A227898

Adjacent sequences: A025831 A025832 A025833 * A025835 A025836 A025837

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved