A029117 Expansion of 1/((1-x)(1-x^7)(1-x^8)(1-x^9)).

1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 4, 5, 6, 8, 9, 10, 10, 10, 11, 12, 14, 16, 18, 19, 20, 21, 22, 24, 26, 29, 31, 33, 35, 37, 39, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 72, 76, 80, 84, 88, 92, 96, 100, 105, 110, 115

Offset

0,8

Links

Table of n, a(n) for n=0..58.

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

Formula

G.f.: 1/((1-x)*(1-x^7)*(1-x^8)*(1-x^9)).

a(n) = a(n-1) + a(n-7) - a(n-10) - a(n-15) + a(n-18) + a(n-24) - a(n-25). - Wesley Ivan Hurt, Mar 07 2022

Mathematica

CoefficientList[Series[1/((1-x)(1-x^7)(1-x^8)(1-x^9)), {x, 0, 60}], x] (* or *) LinearRecurrence[ {1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 4, 5, 6, 8, 9, 10, 10, 10, 11, 12, 14, 16}, 60] (* Harvey P. Dale, May 21 2023 *)

Prog

(PARI) Vec(1/((1-x)*(1-x^7)*(1-x^8)*(1-x^9)) + O(x^99)) \\ Jinyuan Wang, Mar 18 2020

Crossrefs

Sequence in context: A131754 A287422 A120510 * A308547 A195850 A253593

Adjacent sequences: A029114 A029115 A029116 * A029118 A029119 A029120

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved