A157614 a(n) = 29282*n^2 + 484*n + 1.

29767, 118097, 264991, 470449, 734471, 1057057, 1438207, 1877921, 2376199, 2933041, 3548447, 4222417, 4954951, 5746049, 6595711, 7503937, 8470727, 9496081, 10579999, 11722481, 12923527, 14183137, 15501311, 16878049, 18313351

Offset

1,1

Comments

The identity (29282*n^2 + 484*n + 1)^2 - (121*n^2 + 2*n)*(2662*n + 22)^2 = 1 can be written as a(n)^2 - A181679(n)*A157613(n)^2 = 1 (see also Bruno Berselli's comment at A181679). - Vincenzo Librandi, Feb 21 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

From Vincenzo Librandi, Feb 21 2012: (Start)

G.f: x*(-29767 - 28796*x - x^2)/(x-1)^3;

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

Mathematica

LinearRecurrence[{3, -3, 1}, {29767, 118097, 264991}, 50] (* Vincenzo Librandi, Feb 21 2012 *)

Prog

(Magma) I:=[29767, 118097, 264991]; [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, Feb 21 2012
(PARI) for(n=1, 40, print1(29282*n^2+484*n+1", ")); \\ Vincenzo Librandi, Feb 21 2012

Crossrefs

Cf. A181679, A157613.

Sequence in context: A251054 A206070 A056747 * A209812 A258755 A251681

Adjacent sequences: A157611 A157612 A157613 * A157615 A157616 A157617

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 03 2009

Status

approved