A025913 Expansion of 1/((1-x^7)*(1-x^9)*(1-x^11)).

1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 1, 0, 2, 0, 2, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 6, 5, 6, 5, 6, 6, 6, 6

Offset

0,19

Comments

Number of partitions of n into parts 7, 9, and 11. - Hoang Xuan Thanh, Sep 26 2025

Links

Table of n, a(n) for n=0..79.

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

Formula

a(n) = floor((9*n^2+n+4)/11) + floor((n^2+5)/9) - floor((13*n^2+n+6)/14) + floor((n+9)/9) - floor((n+8)/9). - Hoang Xuan Thanh, Sep 26 2025

Mathematica

CoefficientList[Series[1/((1-x^7)(1-x^9)(1-x^11)), {x, 0, 120}], x] (* Harvey P. Dale, Aug 07 2019 *)

Prog

(PARI) a(n) = (n^2+27*n+680)/1386 + ((3*n^2+4*n+3)%7)/7 - ((9*n^2+n+4)%11)/11 - ((n^2+5)%9)/9 + (n%9==0) \\ Hoang Xuan Thanh, Sep 26 2025

Crossrefs

Sequence in context: A115382 A112202 A126205 * A123230 A078821 A125184

Adjacent sequences: A025910 A025911 A025912 * A025914 A025915 A025916

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved