A025823 Expansion of 1/((1-x^2)*(1-x^9)*(1-x^10)).

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

Offset

0,11

Comments

Number of partitions of n into parts 2, 9, and 10. - Hoang Xuan Thanh, Sep 02 2025

Links

Table of n, a(n) for n=0..71.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,0,0,0,1,1,-1,-1,0,0,0,0,0,0,-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)=0, a(8)=1, a(9)=1, a(10)=2, a(11)=1, a(12)=2, a(13)=1, a(14)=2, a(15)=1, a(16)=2, a(17)=1, a(18)=3, a(19)=2, a(20)=4, a(n)=a(n-2)+a(n-9)+a(n-10)- a(n-11)- a(n-12)-a(n-19)+a(n-21). - Harvey P. Dale, Oct 15 2013

a(n) = floor((n^2 + 21*n + 254)/360 + (n+8)*(-1)^n/40 + (((n+9) mod 10) - ((n+1) mod 10))/24). - Hoang Xuan Thanh, Sep 02 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^9)(1-x^10)), {x, 0, 80}], x] (* or *) LinearRecurrence[{0, 1, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 0, 1}, {1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4}, 80] (* Harvey P. Dale, Oct 15 2013 *)

Prog

(PARI) Vec(1/((1-x^2)*(1-x^9)*(1-x^10)) + O(x^70)) \\ Hoang Xuan Thanh, Sep 02 2025

Crossrefs

Sequence in context: A247599 A083897 A368212 * A025821 A161233 A161057

Adjacent sequences: A025820 A025821 A025822 * A025824 A025825 A025826

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved