A145332 Numbers Y such that 129*Y^2+43 is a square.

53, 1786683, 60229083877, 2030322415706987, 68442168573253447893, 2307185500574051312766043, 77775223155909101180089861637, 2621802770278510300206777923017227, 88380971308313359064061382604820860533

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).

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: A367766 A336440 A368298 * 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