A025846 Expansion of 1/((1-x^3)*(1-x^7)*(1-x^9)).

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

Offset

0,10

Comments

Number of partitions of n into parts 3, 7, and 9. - Hoang Xuan Thanh, Sep 05 2025

Links

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

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

Formula

G.f.: 1/((1-x^3)*(1-x^7)*(1-x^9)).

a(n) = floor((n^2 + 33*n + 273)/378 - (n+4)*(n mod 3)/27 + (4/27)*((n+2) mod 3) + (2/63)*(((n+7) mod 9)-((n+6) mod 9))). - Hoang Xuan Thanh, Sep 05 2025

Mathematica

CoefficientList[Series[1/((1-x^3)(1-x^7)(1-x^9)), {x, 0, 80}], x] (* Harvey P. Dale, Sep 07 2011 *)

Prog

(PARI) a(n) = (n^2 + 33*n + 273 - 14*(n+4)*(n%3) + 56*((n+2)%3) + 12*(((n+7)%9) - ((n+6)%9))) \378 \\ Hoang Xuan Thanh, Sep 05 2025

Crossrefs

Sequence in context: A279792 A025852 A190762 * A241272 A358991 A033780

Adjacent sequences: A025843 A025844 A025845 * A025847 A025848 A025849

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved