A157288 a(n) = 10368*n^2 - 288*n + 1.

10081, 40897, 92449, 164737, 257761, 371521, 506017, 661249, 837217, 1033921, 1251361, 1489537, 1748449, 2028097, 2328481, 2649601, 2991457, 3354049, 3737377, 4141441, 4566241, 5011777, 5478049, 5965057, 6472801, 7001281

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 a(n)^2 - A157286(n)*A157287(n)^2 = 1 (see also second part of the comment at 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 (3,-3,1).

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 28 2012

G.f.: x*(-10081 - 10654*x - x^2)/(x-1)^3. - Vincenzo Librandi, Jan 28 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {10081, 40897, 92449}, 40] (* Vincenzo Librandi, Jan 28 2012 *)

Prog

(Magma) I:=[10081, 40897, 92449]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 28 2012
(PARI) for(n=1, 40, print1(10368*n^2 - 288*n + 1", ")); \\ Vincenzo Librandi, Jan 28 2012

Crossrefs

Cf. A157286, A157287.

Sequence in context: A190293 A179729 A217867 * A230033 A252052 A083965

Adjacent sequences: A157285 A157286 A157287 * A157289 A157290 A157291

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 27 2009

Status

approved