A145318 Numbers X such that exists Y in N with X^2 = 93*Y^2+31.

434, 10546634, 256304299034, 6228707064577634, 151370038827061362434, 3678594677346538165293434, 89397207697505531665899670634, 2172530937786184753198155630454034, 52796846760682654174716046465394263634, 1283068967805578923967764608003855764379434

Offset

1,1

Links

Colin Barker, 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.: -434*x*(x-1)/(x^2-24302*x+1). - Colin Barker, Aug 23 2012

Example

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

Mathematica

CoefficientList[Series[434 (1 - x)/(x^2 - 24302 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 01 2014 *)
LinearRecurrence[{24302, -1}, {434, 10546634}, 20] (* Harvey P. Dale, Mar 04 2019 *)

Prog

(PARI) Vec(-434*x*(x-1)/(x^2-24302*x+1) + O(x^100)) \\ Colin Barker, Nov 01 2014
(Magma) I:=[434, 10546634]; [n le 2 select I[n] else 24302*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi Nov 01 2014

Crossrefs

Sequence in context: A237386 A259294 A050507 * A054987 A054905 A160353

Adjacent sequences: A145315 A145316 A145317 * A145319 A145320 A145321

Keyword

easy,nonn

Author

Richard Choulet, Oct 07 2008

Status

approved