A157858 a(n) = 1728000*n - 240.

1727760, 3455760, 5183760, 6911760, 8639760, 10367760, 12095760, 13823760, 15551760, 17279760, 19007760, 20735760, 22463760, 24191760, 25919760, 27647760, 29375760, 31103760, 32831760, 34559760, 36287760, 38015760

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 A157859(n)^2 - A157857(n)*a(n)^2 = 1. - Vincenzo Librandi, Jan 25 2012

This is the case s=60 of the identity (8*n^2*s^4 - 8*n*s^2 + 1)^2 - (n^2*s^2 - n)*(8*n*s^3 - 4*s)^2 = 1. - Bruno Berselli, 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*(1727760 + 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}, {1727760, 3455760}, 40] (* Vincenzo Librandi, Jan 25 2012 *)

Prog

(Magma) I:=[1727760, 3455760]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Jan 25 2012
(PARI) for(n=1, 22, print1(1728000*n - 240", ")); \\ Vincenzo Librandi, Jan 25 2012

Crossrefs

Cf. A157857, A157859.

Sequence in context: A233633 A151639 A083646 * A157862 A186586 A131639

Adjacent sequences: A157855 A157856 A157857 * A157859 A157860 A157861

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 08 2009

Status

approved