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A157613 a(n) = 2662*n + 22. 3
2684, 5346, 8008, 10670, 13332, 15994, 18656, 21318, 23980, 26642, 29304, 31966, 34628, 37290, 39952, 42614, 45276, 47938, 50600, 53262, 55924, 58586, 61248, 63910, 66572, 69234, 71896, 74558, 77220, 79882, 82544, 85206, 87868, 90530 (list; graph; refs; listen; history; text; internal format)
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 A157614(n)^2 - A181679(n)*a(n)^2 = 1 (see also Bruno Berselli's comment in 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 (2,-1).

FORMULA

From Vincenzo Librandi, Feb 21 2012: (Start)

G.f.: x*(2684 - 22*x)/(1-x)^2;

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

MATHEMATICA

LinearRecurrence[{2, -1}, {2684, 5346}, 50] (* Vincenzo Librandi, Feb 21 2012 *)

PROG

(Magma) I:=[2684, 5346]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 21 2012

(PARI) for(n=1, 50, print1(2662*n + 22", ")); \\ Vincenzo Librandi, Feb 21 2012

CROSSREFS

Cf. A157614, A181679.

Sequence in context: A236594 A217335 A243993 * A233899 A350184 A186833

Adjacent sequences: A157610 A157611 A157612 * A157614 A157615 A157616

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 03 2009

STATUS

approved

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Last modified December 3 23:46 EST 2022. Contains 358544 sequences. (Running on oeis4.)