A157460 Expansion of 88*x^2 / (1-483*x+483*x^2-x^3).

0, 88, 42504, 20486928, 9874656880, 4759564129320, 2294100035675448, 1105751457631436704, 532969908478316815968, 256890390135091073859960, 123820635075205419283684840, 59681289215858877003662233008, 28766257581408903510345912625104

Offset: 1

Author

Paul Weisenhorn, Mar 01 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.

A157460 is the c(n) sequence for A=5.

Links

• Colin Barker, Table of n, a(n) for n = 1..350
• Index entries for linear recurrences with constant coefficients, signature (483,-483,1).

Crossrefs

5*A157460(n)+1 = A157014(n)^2 for n>=1.

6*A157460(n)+1 = A133283(n)^2 for n>=1.

Programs

Mathematica

CoefficientList[Series[88x^2/(1-483x+483x^2-x^3),{x,0,30}],x] (* or *) LinearRecurrence[{483,-483,1},{0,0,88},30] (* Harvey P. Dale, Apr 16 2015 *)

PARI

concat(0, Vec(88*x^2/(1-483*x+483*x^2-x^3)+O(x^20))) \\ Charles R Greathouse IV, Sep 26 2012

PARI

a(n) = round(-((241+44*sqrt(30))^(-n)*(-1+(241+44*sqrt(30))^n)*(11+2*sqrt(30)+(-11+2*sqrt(30))*(241+44*sqrt(30))^n))/120) \\ Colin Barker, Jul 25 2016

Formula

G.f.: 88*x^2 / (1-483*x+483*x^2-x^3).

c(1) = 0, c(2) = 88, c(3) = 483*c(2), c(n) = 483*(c(n-1)-c(n-2))+c(n-3) for n>3.

a(n) = -((241+44*sqrt(30))^(-n)*(-1+(241+44*sqrt(30))^n)*(11+2*sqrt(30)+(-11+2*sqrt(30))*(241+44*sqrt(30))^n))/120. - Colin Barker, Jul 25 2016

Extensions

Edited by Alois P. Heinz, Sep 09 2011