A025909 Expansion of 1/((1-x^7)*(1-x^8)*(1-x^10)).

1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 4, 5, 4, 5, 4, 5, 4, 5, 5, 6, 5, 6, 5, 6, 5, 7, 6, 7, 6, 7, 6, 7, 7, 8, 7

Offset

0,25

Comments

Number of partitions of n into parts 7, 8, and 10. - Hoang Xuan Thanh, Sep 25 2025

Links

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

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

Formula

a(n) = floor((n^2+25*n+445 + 7*(n+5)*(-1)^n)/1120 + ((n+2)^2 mod 7)/7). - Hoang Xuan Thanh, Sep 25 2025

Mathematica

CoefficientList[Series[1/((1-x^7)(1-x^8)(1-x^10)), {x, 0, 80}], x] (* Harvey P. Dale, Oct 26 2011 *)

Prog

(PARI) a(n) = ((n^2+25*n+445 + 7*(n+5)*(-1)^n)/1120 + ((n+2)^2%7)/7)\1 \\ Hoang Xuan Thanh, Sep 25 2025

Crossrefs

Cf. A025908, A025910.

Sequence in context: A196942 A184304 A363298 * A025899 A025869 A093320

Adjacent sequences: A025906 A025907 A025908 * A025910 A025911 A025912

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved