A157880 Expansion of 136*x^2 / (-x^3+1155*x^2-1155*x+1).

0, 136, 157080, 181270320, 209185792336, 241400223085560, 278575648254944040, 321476056685982336736, 370983090839975361649440, 428114165353274881361117160, 494043375834588373115367553336, 570125627598949629300252795432720, 657924480205812037624118610561805680

Offset: 1

Author

Paul Weisenhorn, Mar 08 2009

Keywords

• nonn
• easy

Comments

This sequence is part of a solution of a more general problem involving two equations, three sequences a(n), b(n), c(n) and a constant A:

A * c(n)+1 = a(n)^2,

(A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.

A157880 is the c(n) sequence for A=8.

Links

• Colin Barker, Table of n, a(n) for n = 1..325
• Index entries for linear recurrences with constant coefficients, signature (1155,-1155,1).

Crossrefs

8*A157880(n)+1 = A077420(n-1)^2.

9*A157880(n)+1 = A046176(n)^2.

Programs

Mathematica

LinearRecurrence[{1155,-1155,1},{0,136,157080},20] (* Harvey P. Dale, Dec 04 2019 *)

PARI

concat(0, Vec(136*x^2/(-x^3+1155*x^2-1155*x+1) + O(x^20))) \\ Charles R Greathouse IV, Sep 26 2012

PARI

a(n) = round(-((577+408*sqrt(2))^(-n)*(-1+(577+408*sqrt(2))^n)*(17+12*sqrt(2)+(-17+12*sqrt(2))*(577+408*sqrt(2))^n))/288) \\ Colin Barker, Jul 25 2016

Formula

G.f.: 136*x^2/(-x^3+1155*x^2-1155*x+1).

c(1) = 0, c(2) = 136, c(3) = 1155*c(2), c(n) = 1155 * (c(n-1)-c(n-2)) + c(n-3) for n>3.

a(n) = -((577+408*sqrt(2))^(-n)*(-1+(577+408*sqrt(2))^n)*(17+12*sqrt(2)+(-17+12*sqrt(2))*(577+408*sqrt(2))^n))/288. - Colin Barker, Jul 25 2016

Extensions

Edited by Alois P. Heinz, Sep 09 2011