A025865 Expansion of 1/((1-x^4)*(1-x^6)*(1-x^9)).

1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 3, 1, 4, 2, 3, 3, 4, 2, 5, 3, 4, 4, 5, 3, 7, 4, 5, 5, 7, 4, 8, 5, 7, 7, 8, 5, 10, 7, 8, 8, 10, 7, 12, 8, 10, 10, 12, 8, 14, 10, 12, 12, 14, 10, 16, 12, 14, 14, 16, 12

Offset

0,13

Comments

Number of partitions of n into parts 4,6, and 9. - Hoang Xuan Thanh, Sep 10 2025

Links

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

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

Formula

a(n) = floor((n^2 + 27*n + 432)/432 + (n+8)*(-1)^n/48 - (n+15)*(n mod 3)/54). - Hoang Xuan Thanh, Sep 10 2025

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^6)(1-x^9)), {x, 0, 80}], x] (* Harvey P. Dale, Nov 03 2011 *)

Prog

(PARI) a(n)=(n^2+27*n+432 + 9*(n+8)*(-1)^n - 8*(n+15)*(n%3))\432 \\ Hoang Xuan Thanh, Sep 10 2025

Crossrefs

Sequence in context: A300831 A068347 A284556 * A085091 A345994 A052128

Adjacent sequences: A025862 A025863 A025864 * A025866 A025867 A025868

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved