A025872 Expansion of 1/((1-x^4)*(1-x^8)*(1-x^9)).

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

Offset

0,9

Comments

Number of partitions of n into parts 4, 8, and 9. - Hoang Xuan Thanh, Sep 13 2025

Links

Table of n, a(n) for n=0..75.

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

Formula

a(n) = floor((n+8)*(n+40)/576 - (n+4)*(n mod 4)/32 + ((8*n^2+6*n+4) mod 9)/9). - Hoang Xuan Thanh, Sep 13 2025

Mathematica

CoefficientList[Series[1/((1-x^4)(1-x^8)(1-x^9)), {x, 0, 80}], x] (* Harvey P. Dale, Jul 05 2011 *)
LinearRecurrence[{0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 3, 2, 1, 0, 3}, 80] (* Harvey P. Dale, Jan 14 2022 *)

Crossrefs

Sequence in context: A257399 A168313 A072575 * A280125 A339060 A280586

Adjacent sequences: A025869 A025870 A025871 * A025873 A025874 A025875

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved