A157862 - OEIS

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A157862

a(n) = 1728000*n + 240.

1728240, 3456240, 5184240, 6912240, 8640240, 10368240, 12096240, 13824240, 15552240, 17280240, 19008240, 20736240, 22464240, 24192240, 25920240, 27648240, 29376240, 31104240, 32832240, 34560240, 36288240, 38016240

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OFFSET

1,1

COMMENTS

The identity (103680000*n^2 + 28800*n + 1)^2 - (3600*n^2 + n)*(1728000*n + 240)^2 = 1 can be written as A157863(n)^2 - A157861(n)*a(n)^2 = 1. - Vincenzo Librandi, Jan 25 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

G.f.: x*(1728240 - 240*x)/(1-x)^2. - Colin Barker, Jan 17 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 25 2012

MATHEMATICA

LinearRecurrence[{2, -1}, {1728240, 3456240}, 40] (* Vincenzo Librandi, Jan 25 2012 *)

PROG

(Magma) I:=[1728240, 3456240]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jan 25 2012

(PARI) for(n=1, 22, print1(1728000*n + 240", ")); \\ Vincenzo Librandi, Jan 25 2012