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A158593 a(n) = 38*n^2 + 1. 2
1, 39, 153, 343, 609, 951, 1369, 1863, 2433, 3079, 3801, 4599, 5473, 6423, 7449, 8551, 9729, 10983, 12313, 13719, 15201, 16759, 18393, 20103, 21889, 23751, 25689, 27703, 29793, 31959, 34201, 36519, 38913, 41383, 43929, 46551, 49249, 52023, 54873 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The identity (38*n^2 + 1)^2 - (361*n^2 + 19)*(2*n)^2 = 1 can be written as a(n)^2 - A158592(n)*A005843(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

G.f.: -(1 + 36*x + 39*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1, 39, 153}, 50] (* Vincenzo Librandi, Feb 16 2012 *)

PROG

(MAGMA) I:=[1, 39, 153]; [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 16 2012

(PARI) for(n=0, 40, print1(38*n^2 + 1", ")); \\ Vincenzo Librandi, Feb 16 2012

CROSSREFS

Cf. A005843, A158592.

Sequence in context: A072253 A128826 A240902 * A158598 A105838 A251335

Adjacent sequences:  A158590 A158591 A158592 * A158594 A158595 A158596

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 22 2009

EXTENSIONS

Comment rewritten, formula replaced by R. J. Mathar, Oct 28 2009

STATUS

approved

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)