A157881 Expansion of 152*x^2 / (-x^3+1443*x^2-1443*x+1).

0, 152, 219336, 316282512, 456079163120, 657665836936680, 948353680783529592, 1367525350024012735136, 1971970606380945580536672, 2843580246875973503121146040, 4100440744024547410555112053160, 5912832709303150490046968459510832

Offset: 1

Author

Paul Weisenhorn, Mar 08 2009, Jun 25 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.

A157881 is the c(n) sequence for A=9.

Links

• Colin Barker, Table of n, a(n) for n = 1..300
• Index entries for linear recurrences with constant coefficients, signature (1443,-1443,1).

Crossrefs

8*A157881(n)+1 = A097315(n-1)^2.

9*A157881(n)+1 = A097314(n-1)^2.

Programs

Mathematica

LinearRecurrence[{1443,-1443,1},{0,152,219336},20] (* Harvey P. Dale, Jul 18 2019 *)

PARI

concat(0, Vec(152*x^2/(-x^3+1443*x^2-1443*x+1) + O(x^20))) \\ Charles R Greathouse IV, Sep 26 2012

PARI

a(n) = round(-((721+228*sqrt(10))^(-n)*(-1+(721+228*sqrt(10))^n)*(19+6*sqrt(10)+(-19+6*sqrt(10))*(721+228*sqrt(10))^n))/360) \\ Colin Barker, Jul 25 2016

Formula

G.f.: 152*x^2/(-x^3+1443*x^2-1443*x+1).

c(1) = 0, c(2) = 152, c(3) = 1443*c(2), c(n) = 1443 * (c(n-1)-c(n-2)) + c(n-3) for n>3.

a(n) = -((721+228*sqrt(10))^(-n)*(-1+(721+228*sqrt(10))^n)*(19+6*sqrt(10)+(-19+6*sqrt(10))*(721+228*sqrt(10))^n))/360. - Colin Barker, Jul 25 2016

Extensions

Edited by Alois P. Heinz, Sep 09 2011