A025818 Expansion of 1/((1-x^2)*(1-x^7)*(1-x^10)).

1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 2, 3, 2, 4, 3, 4, 3, 5, 3, 5, 4, 6, 4, 7, 5, 7, 5, 8, 6, 8, 7, 9, 7, 10, 8, 11, 8, 12, 9, 12, 10, 13, 11, 14, 12, 15, 12, 16, 13, 17, 14, 18, 15, 19, 16, 20, 17, 21, 18, 22, 19, 23

Offset

0,11

Comments

Number of partitions of n into parts 2, 7, and 10. - Hoang Xuan Thanh, Aug 31 2025

Links

Table of n, a(n) for n=0..68.

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

Formula

a(0)=1, a(1)=0, a(2)=1, a(3)=0, a(4)=1, a(5)=0, a(6)=1, a(7)=1, a(8)=1, a(9)=1, a(10)=2, a(11)=1, a(12)=2, a(13)=1, a(14)=3, a(15)=1, a(16)=3, a(17)=2, a(18)=3, a(n)=a(n-2)+a(n-7)-a(n-9)+a(n-10)-a(n-12)- a(n-17)+ a(n-19). - Harvey P. Dale, Sep 21 2013

a(n) = floor((n^2 + 19*n + 217 + 7*(n+9)*(-1)^n)/280). Hoang Xuan Thanh, Aug 31 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^7)(1-x^10)), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1}, {1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 2, 3}, 100] (* Harvey P. Dale, Sep 21 2013 *)

Prog

(PARI) a(n) = (n^2 +19*n +217 +7*(n+9)*(-1)^n)\280 \\ Hoang Xuan Thanh, Aug 31 2025

Crossrefs

Sequence in context: A385662 A138012 A072531 * A324938 A362181 A079413

Adjacent sequences: A025815 A025816 A025817 * A025819 A025820 A025821

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved