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A145332 Numbers Y such that 129*Y^2+43 is a square. 1
53, 1786683, 60229083877, 2030322415706987, 68442168573253447893, 2307185500574051312766043, 77775223155909101180089861637, 2621802770278510300206777923017227, 88380971308313359064061382604820860533 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (33710,-1).

FORMULA

a(n+2) = 33710*a(n+1)-a(n).

a(n) = (53/2)*{[16855+1484*sqrt(129)]^n+[16855-1484*sqrt(129)]^n}-(7/3)*sqrt(129)*{[16855-1484*sqrt(129)]^n-[16855 +1484*sqrt(129)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: 53*x*(x+1) / (x^2-33710*x+1). - Colin Barker, Oct 21 2014

EXAMPLE

a(1)=53 because the first relation is : 602^2=129*53^2+43.

MATHEMATICA

LinearRecurrence[{33710, -1}, {53, 1786683}, 20] (* Harvey P. Dale, Jan 21 2014 *)

CoefficientList[Series[53 (x + 1)/(x^2 - 33710 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

PROG

(PARI) Vec(53*x*(x+1)/(x^2-33710*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014

(MAGMA) I:=[53, 1786683]; [n le 2 select I[n] else 33710*Self(n-1)-Self(n-2): n in [1..10]]; // Vincenzo Librandi, Oct 21 2014

CROSSREFS

Sequence in context: A169595 A183793 A336440 * A087530 A125037 A101365

Adjacent sequences:  A145329 A145330 A145331 * A145333 A145334 A145335

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 08 2008

EXTENSIONS

Editing from Colin Barker, Oct 21 2014

STATUS

approved

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Last modified June 29 14:46 EDT 2022. Contains 354913 sequences. (Running on oeis4.)