A157287 a(n) = 1728*n - 24.

1704, 3432, 5160, 6888, 8616, 10344, 12072, 13800, 15528, 17256, 18984, 20712, 22440, 24168, 25896, 27624, 29352, 31080, 32808, 34536, 36264, 37992, 39720, 41448, 43176, 44904, 46632, 48360, 50088, 51816, 53544, 55272, 57000, 58728

Offset

1,1

Comments

The identity (10368*n^2 - 288*n + 1)^2 - (36*n^2-n)*(1728*n-24)^2 = 1 can be written as A157288(n)^2 - A157286(n)*a(n)^2 = 1 (see also second part of the initial comment in A157286). - Vincenzo Librandi, Jan 28 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

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 28 2012

G.f.: x*(24*x+1704)/(x-1)^2. - Vincenzo Librandi, Jan 28 2012

Mathematica

LinearRecurrence[{2, -1}, {1704, 3432}, 40] (* Vincenzo Librandi, Jan 28 2012 *)

Prog

(Magma) I:=[1704, 3432]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 28 2012
(PARI) for(n=1, 40, print1(1728*n-24", ")); \\ Vincenzo Librandi, Jan 28 2012

Crossrefs

Cf. A157286, A157288.

Sequence in context: A210121 A345506 A345782 * A029559 A222553 A345516

Adjacent sequences: A157284 A157285 A157286 * A157288 A157289 A157290

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 27 2009

Extensions

Comment rewritten by Bruno Berselli, Jan 28 2012

Status

approved