A025789 Expansion of 1/((1-x)*(1-x^8)*(1-x^9)).

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 6, 6, 7, 8, 9, 10, 10, 10, 10, 10, 11, 12, 13, 14, 15, 15, 15, 15, 16, 17, 18, 19, 20, 21, 21, 21, 22, 23, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 33, 34, 35

Offset

0,9

Comments

Number of partitions of n into parts 1, 8, and 9. - Hoang Xuan Thanh, Aug 15 2025

Links

Table of n, a(n) for n=0..62.

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

Formula

a(n) = (n^2 + 18*n + 9*(2+(n mod 8))*(8-(n mod 8)) - 8*(n mod 9)*(9-(n mod 9)))/144. - Hoang Xuan Thanh, Aug 19 2025

Mathematica

CoefficientList[Series[1/((1-x)(1-x^8)(1-x^9)), {x, 0, 70}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, -1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 4, 5}, 70] (* Harvey P. Dale, Dec 09 2025 *)

Prog

(PARI) b(m) = if(m>0, 9*(m-2)*(m-8), 0);
c(x, y) = 81-x^2 + b((x+1)%8) - b((x+y-6)%8);
a(n) = (n^2 + 18*n + c(n%9, n\9))/144 \\ Hoang Xuan Thanh, Aug 15 2025

Crossrefs

Sequence in context: A072292 A243282 A093390 * A080585 A295977 A089361

Adjacent sequences: A025786 A025787 A025788 * A025790 A025791 A025792

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved