A025791 Expansion of 1/((1-x)*(1-x^9)*(1-x^10)).

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

Offset

0,10

Comments

Number of partitions of n into parts 1, 9, and 10. - Hoang Xuan Thanh, Aug 19 2025

Links

Table of n, a(n) for n=0..63.

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

Formula

a(n) = a(n-1)-a(n-19)+a(n-20). - Harvey P. Dale, Jan 14 2016

a(n) = (n^2 + 20*n + 10*(2+(n mod 9))*(9-(n mod 9)) - 9*(n mod 10)*(10-(n mod 10)))/180. - Hoang Xuan Thanh, Aug 19 2025

Mathematica

CoefficientList[Series[1/((1-x)(1-x^9)(1-x^10)), {x, 0, 70}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5}, 70] (* Harvey P. Dale, Jan 14 2016 *)

Prog

(PARI) Vec( 1/((1-x)*(1-x^9)*(1-x^10)) + O(x^65) ) \\ Hoang Xuan Thanh, Aug 19 2025

Crossrefs

Sequence in context: A354760 A025793 A102680 * A358474 A324608 A237115

Adjacent sequences: A025788 A025789 A025790 * A025792 A025793 A025794

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved