A145319 Numbers Y such that 93*Y^2+31 is a square.

45, 1093635, 26577517725, 645886834659315, 15696341829313155405, 381452498490081467992995, 9270058602609618005852609085, 225280963779166438288148637990675, 5474777972491244180668970194596774765, 133048054062201252299450875380942182348355

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (24302,-1).

Formula

a(n+2) = 24302*a(n+1)-a(n).

G.f.: 45*x*(x+1) / (x^2-24302*x+1). - Colin Barker, Oct 21 2014

Example

a(1)=45 because the first relation is : 434^2=93*45^2+31.

Mathematica

CoefficientList[Series[45 (x + 1)/(x^2 - 24302 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)
LinearRecurrence[{24302, -1}, {45, 1093635}, 20] (* Harvey P. Dale, Jun 15 2022 *)

Prog

(PARI) Vec(45*x*(x+1) / (x^2-24302*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014
(Magma) I:=[45, 1093635]; [n le 2 select I[n] else 24302*Self(n-1)-Self(n-2): n in [1..10]]; // Vincenzo Librandi, Oct 21 2014

Crossrefs

Sequence in context: A354362 A003739 A300198 * A089626 A110479 A023934

Adjacent sequences: A145316 A145317 A145318 * A145320 A145321 A145322

Keyword

easy,nonn

Author

Richard Choulet, Oct 07 2008

Extensions

Editing and more terms from Colin Barker, Oct 21 2014

Status

approved