A025861 Expansion of 1/((1-x^4)*(1-x^5)*(1-x^9)).

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

Offset

0,10

Comments

Number of partitions of n into parts 4, 5, and 9. - Hoang Xuan Thanh, Sep 09 2025

Links

Table of n, a(n) for n=0..70.

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

Formula

a(n) = floor((n+9)^2/360 + (((2*n^2+1) mod 9) + ((n+8) mod 9) - (n mod 9) + ((n+4) mod 5) - ((n+3) mod 5))/9). - Hoang Xuan Thanh, Sep 09 2025

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^5)(1-x^9)), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 2, 1, 1, 2}, 100] (* Harvey P. Dale, Aug 01 2021 *)

Prog

(PARI) a(n) = ((n+9)^2 + 40*(((2*n^2+1)%9) + ((n+8)%9) - (n%9) + ((n+4)%5) - ((n+3)%5)))\360 \\ Hoang Xuan Thanh, Sep 09 2025

Crossrefs

Sequence in context: A282318 A286971 A380855 * A090723 A027357 A256479

Adjacent sequences: A025858 A025859 A025860 * A025862 A025863 A025864

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved