A025817 Expansion of 1/((1-x^2)*(1-x^7)*(1-x^9)).

1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 3, 2, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 5, 6, 6, 6, 7, 6, 8, 7, 9, 8, 9, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 23, 23, 24, 25, 25, 27, 26, 28, 27

Offset

0,10

Comments

Number of partitions of n into parts 2, 7, and 9. - Hoang Xuan Thanh, Aug 30 2025

Links

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

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

Formula

a(n) = floor((n^2 + 18*n + 290)/252 - (n mod 2)/4 + (5/18)*[(n mod 9)=0] - (3/7)*([(n mod 7) in {0,3,5}] + [(n mod 7)=5])). - Hoang Xuan Thanh, Aug 30 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^7)(1-x^9)), {x, 0, 80}], x] (* Harvey P. Dale, Oct 13 2024 *)

Prog

(PARI) a(n) = (n^2 +18*n +290 -63*(n%2) -108*[1, 0, 0, 1, 0, 2, 0][n%7+1] +70*(n%9==0))\252 \\ Hoang Xuan Thanh, Aug 30 2025

Crossrefs

Sequence in context: A133989 A379375 A029398 * A109381 A058506 A325509

Adjacent sequences: A025814 A025815 A025816 * A025818 A025819 A025820

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved