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A075871 Numbers n such that 13*n^2 + 1 is a square. 4
0, 180, 233640, 303264540, 393637139280, 510940703520900, 663200639532988920, 860833919173116097260, 1117361763886065161254560, 1450334708690193406192321620, 1882533334518107155172472208200, 2443526817869794397220462733921980 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Lim_{n-> Inf.} a(n)/a(n-1) = 649 + 180*Sqrt(13).

This sequence gives the values of y in solutions of the Diophantine equation x^2 - 13*y^2 = 1. The corresponding x values are in A114047. - Vincenzo Librandi, Aug 08 2010, edited by Jon E. Schoenfield, May 04 2014

LINKS

Colin Barker, Table of n, a(n) for n = 1..322

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (1298,-1).

FORMULA

a(n) = 1298*a(n-1)-a(n-2), n>1. - Michael Somos, Oct 30 2002

a(n) = [(649+180*sqrt(13))^n - (649-180*sqrt(13))^n] / (2*sqrt(13)).

a(n) = 1297*(a(n-1)+a(n-2))-a(n-3). a(n) = 1299*(a(n-1)-a(n-2))+a(n-3). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 20 2006

G.f.: 180*x^2/(1-1298*x+x^2). - Philippe Deléham, Nov 18 2008

MATHEMATICA

LinearRecurrence[{1298, -1}, {0, 180}, 50] (* Vincenzo Librandi, Jun 14 2015 *)

PROG

(PARI) concat(0, Vec(180*x^2/(1-1298*x+x^2) + O(x^20))) \\ Colin Barker, Jun 13 2015

(MAGMA) I:=[0, 180]; [n le 2 select I[n] else 1298*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 14 2015

CROSSREFS

Cf. A114047.

Cf. A202156.

Sequence in context: A091033 A146530 A057867 * A177327 A236235 A225349

Adjacent sequences:  A075868 A075869 A075870 * A075872 A075873 A075874

KEYWORD

nonn,easy

AUTHOR

Gregory V. Richardson, Oct 16 2002

STATUS

approved

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Last modified May 23 07:01 EDT 2017. Contains 286909 sequences.