A025843 Expansion of 1/((1-x^3)*(1-x^6)*(1-x^10)).

1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 3, 1, 0, 3, 2, 0, 4, 2, 1, 4, 3, 1, 5, 3, 2, 5, 4, 2, 7, 4, 3, 7, 5, 3, 9, 5, 4, 9, 7, 4, 11, 7, 5, 11, 9, 5, 13, 9, 7, 13, 11, 7, 15, 11, 9, 15, 13, 9, 18, 13, 11, 18, 15, 11, 21, 15, 13, 21, 18

Offset

0,7

Comments

Number of partitions of n into parts 3, 6, and 10. - Hoang Xuan Thanh, Sep 04 2025

Links

Table of n, a(n) for n=0..70.

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

Formula

a(n) = floor((n+10)*(n+29)/360 + n*(-1)^n/120 - (n+7)*(n mod 3)/18 + (2/9)*((n+2) mod 3)). - Hoang Xuan Thanh, Sep 04 2025

Prog

(PARI) a(n) = (n^2 +39*n +290 +3*n*(-1)^n -20*(n+7)*(n%3) +80*((n+2)%3)) \360 \\ Hoang Xuan Thanh, Sep 04 2025

Crossrefs

Sequence in context: A244738 A331195 A215462 * A303906 A178580 A035437

Adjacent sequences: A025840 A025841 A025842 * A025844 A025845 A025846

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved