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

1,2

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).

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

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 *)

Prog

(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

Crossrefs

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

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

Sequence in context: A174499 A048919 A159718 * A267917 A093244 A079036

Adjacent sequences: A157457 A157458 A157459 * A157461 A157462 A157463

Keyword

nonn,easy

Author

Paul Weisenhorn, Mar 01 2009

Extensions

Edited by Alois P. Heinz, Sep 09 2011

Status

approved