A025868 Expansion of 1/((1-x^4)*(1-x^7)*(1-x^9)).

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

Offset

0,17

Comments

Number of partitions of n into parts 4, 7, and 9. - Hoang Xuan Thanh, Sep 10 2025

Links

Table of n, a(n) for n=0..73.

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

Formula

a(n) = floor((n^2 + 20*n + 288)/504 - (n mod 4)/9 + ((3*n^2+4*n+3) mod 7)/7). - Hoang Xuan Thanh, Sep 10 2025

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^7)(1-x^9)), {x, 0, 80}], x] (* or *) LinearRecurrence[{0, 0, 0, 1, 0, 0, 1, 0, 1, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1}, 80] (* Harvey P. Dale, May 02 2025 *)

Prog

(PARI) a(n) = (n^2+20*n+288 - 56*(n%4) + 72*((3*n^2+4*n+3)%7))\504;

Crossrefs

Sequence in context: A008616 A331973 A097471 * A271721 A050252 A025877

Adjacent sequences: A025865 A025866 A025867 * A025869 A025870 A025871

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved