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A158539 a(n) = 121*n^2 - 11. 2
110, 473, 1078, 1925, 3014, 4345, 5918, 7733, 9790, 12089, 14630, 17413, 20438, 23705, 27214, 30965, 34958, 39193, 43670, 48389, 53350, 58553, 63998, 69685, 75614, 81785, 88198, 94853, 101750, 108889, 116270, 123893, 131758, 139865 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (22*n^2 - 1)^2 - (121*n^2 - 11)*(2*n)^2 = 1 can be written as A158540(n)^2 - a(n)*A005843(n)^2 = 1. - 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.: 11*x*(-10 - 13*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}, {110, 473, 1078}, 50] (* Vincenzo Librandi, Feb 21 2012 *)

PROG

(MAGMA) I:=[110, 473, 1078]; [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(121*n^2 - 11", ")); \\ Vincenzo Librandi, Feb 21 2012

CROSSREFS

Cf. A005843, A158540.

Sequence in context: A028995 A209372 A285984 * A251028 A251021 A251030

Adjacent sequences:  A158536 A158537 A158538 * A158540 A158541 A158542

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 21 2009

EXTENSIONS

Edited by N. J. A. Sloane, Oct 12 2009

STATUS

approved

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Last modified September 22 05:47 EDT 2019. Contains 327287 sequences. (Running on oeis4.)