A157879 Expansion of 120*x^2 / (-x^3+899*x^2-899*x+1).

0, 120, 107880, 96876240, 86994755760, 78121193796360, 70152745034375640, 62997086919675528480, 56571313901123590199520, 50800976886122064323640600, 45619220672423712639039059400, 40966009362859607827792751700720, 36787430788627255405645251988187280

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 2 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.

A157879 is the c(n) sequence for A=7.

Links

• Colin Barker, Table of n, a(n) for n = 1..300
• Index entries for linear recurrences with constant coefficients, signature (899,-899,1).

Crossrefs

7*A157879(n)+1 = A157877(n)^2.

8*A157879(n)+1 = A157878(n)^2.

Cf. A245031.

Programs

Mathematica

CoefficientList[Series[120x^2/(-x^3+899x^2-899x+1),{x,0,30}],x] (* or *) LinearRecurrence[{899,-899,1},{0,0,120},30] (* Harvey P. Dale, Jan 14 2014 *)

PARI

concat(0, Vec(120*x^2/(-x^3+899*x^2-899*x+1)+O(x^20))) \\ Charles R Greathouse IV, Sep 25 2012

PARI

a(n) = round(-((449+120*sqrt(14))^(-n)*(-1+(449+120*sqrt(14))^n)*(15+4*sqrt(14)+(-15+4*sqrt(14))*(449+120*sqrt(14))^n))/224) \\ Colin Barker, Jul 25 2016

Formula

G.f.: 120*x^2/(-x^3+899*x^2-899*x+1).

c(1) = 0, c(2) = 120, c(3) = 899*c(2), c(n) = 899 * (c(n-1)-c(n-2)) + c(n-3) for n>3.

a(n) = -((449+120*sqrt(14))^(-n)*(-1+(449+120*sqrt(14))^n)*(15+4*sqrt(14)+(-15+4*sqrt(14))*(449+120*sqrt(14))^n))/224. - Colin Barker, Jul 25 2016

Extensions

Edited by Alois P. Heinz, Sep 09 2011