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A158640 52*n^2 - 1. 2
51, 207, 467, 831, 1299, 1871, 2547, 3327, 4211, 5199, 6291, 7487, 8787, 10191, 11699, 13311, 15027, 16847, 18771, 20799, 22931, 25167, 27507, 29951, 32499, 35151, 37907, 40767, 43731, 46799, 49971, 53247, 56627, 60111, 63699, 67391 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (52*n^2-1)^2-(676*n^2-26)*(2*n)^2 = 1 can be written as a(n)^2-A158639(n)*A005843(n)^2 =1.

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

G.f.: x*(-51-54*x+x^2)/(x-1)^3.

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

MAPLE

A158640:=n->52*n^2 - 1; seq(A158640(n), n=1..50); # Wesley Ivan Hurt, Feb 22 2014

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {51, 207, 467}, 50] (* Vincenzo Librandi, Feb 17 2012 *)

PROG

(MAGMA) I:=[51, 207, 467]; [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 17 2012

(PARI) for(n=1, 40, print1(52*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 17 2012

CROSSREFS

Cf. A158639, A005843.

Sequence in context: A157365 A157916 A007264 * A107253 A030535 A201813

Adjacent sequences:  A158637 A158638 A158639 * A158641 A158642 A158643

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 23 2009

EXTENSIONS

Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009

STATUS

approved

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Last modified October 18 04:57 EDT 2019. Contains 328145 sequences. (Running on oeis4.)