A228535 x-values in the solution to the Pell equation x^2 - 53*y^2 = -1.

182, 24114818, 3195165155182, 423352992707189818, 56093424824522071350182, 7432266601976172417049224818, 984760460172545468089666118585182, 130478791444509662828968408963250219818, 17288178907829880845340110782723061506860182

Offset

1,1

Comments

All terms are multiples of 182.

Links

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

Index entries for linear recurrences with constant coefficients, signature (132498,-1).

Formula

a(n) = 132498*a(n-1)-a(n-2).

G.f.: 182*x*(x+1) / (x^2-132498*x+1).

Mathematica

CoefficientList[Series[182 (x + 1) / (x^2 - 132498 x + 1), {x, 0, 10}], x] (* Vincenzo Librandi, Aug 25 2013 *)
LinearRecurrence[{132498, -1}, {182, 24114818}, 20] (* Harvey P. Dale, Nov 07 2022 *)

Prog

(PARI) Vec(182*x*(x+1)/(x^2-132498*x+1) + O(x^50))

Crossrefs

Cf. A228536 gives the corresponding y-values.

Sequence in context: A190830 A145525 A028676 * A248628 A217608 A264779

Adjacent sequences: A228532 A228533 A228534 * A228536 A228537 A228538

Keyword

nonn,easy

Author

Colin Barker, Aug 24 2013

Status

approved