A025912 Expansion of 1/((1-x^7)*(1-x^9)*(1-x^10)).

1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 5, 6, 6, 6, 6, 6, 7, 6, 7

Offset

0,28

Comments

Number of partitions of n into parts 7, 9, and 10. - Hoang Xuan Thanh, Sep 26 2025

Links

Table of n, a(n) for n=0..79.

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

Formula

a(n) = floor((7*n^2+2*n+3)/20) + floor((2*n^2+7*n)/9) - floor((4*n^2+6*n-3)/7). - Hoang Xuan Thanh, Sep 26 2025

Prog

(PARI) a(n) = (n^2+26*n+729)/1260 + ((4*n^2+6*n+4)%7)/7 - ((2*n^2+7*n)%9)/9 - ((7*n^2+2*n+3)%20)/20 \\ Hoang Xuan Thanh, Sep 26 2025

Crossrefs

Cf. A025911, A025913.

Sequence in context: A258257 A086600 A218450 * A029441 A342263 A109495

Adjacent sequences: A025909 A025910 A025911 * A025913 A025914 A025915

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved