A025809 Expansion of 1/((1-x^2)*(1-x^5)*(1-x^9)).

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 22, 22, 23, 23, 24, 25, 26, 26, 27, 28, 29, 30

Offset

0,10

Comments

Number of partitions of n into parts 2, 5, and 9. - Hoang Xuan Thanh, Aug 28 2025

Links

Table of n, a(n) for n=0..65.

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

Formula

a(n) = floor((n^2 + 16*n + 234 - 45*(n mod 2) + 18*( ((n+2) mod 5) - ((n+3) mod 5) - 8*(n mod 5) + 2*(n mod 5)^2 ))/180). - Hoang Xuan Thanh, Aug 28 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^5)(1-x^9)), {x, 0, 100}], x] (*  or *) LinearRecurrence[{0, 1, 0, 0, 1, 0, -1, 0, 1, 0, -1, 0, 0, -1, 0, 1}, {1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3}, 100] (* Harvey P. Dale, Aug 24 2016 *)

Prog

(PARI) a(n) = (n^2 +16*n +108 -45*(n%2) + 36*[2, 0, 1, 0, 2][n%5+1])\180 \\ Hoang Xuan Thanh, Aug 28 2025

Crossrefs

Sequence in context: A104277 A125893 A005857 * A204591 A279220 A114575

Adjacent sequences: A025806 A025807 A025808 * A025810 A025811 A025812

Keyword

nonn

Author

N. J. A. Sloane

Status

approved