A281503 Solutions x to the negative Pell equation y^2 = 33*x^2 - 8 with x,y >= 0.

1, 3, 43, 137, 1977, 6299, 90899, 289617, 4179377, 13316083, 192160443, 612250201, 8835201001, 28150193163, 406227085603, 1294296635297, 18677610736737, 59509495030499, 858763866804299, 2736142474767657, 39484460262261017, 125803044344281723

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

M. A. Gopalan, S. Vidhyalakshmi, E. Premalatha, R. Janani, On The Negative Pell Equation y^2 = 33*x^2 - 8, International Journal of Multidisciplinary Research and Modern Education (IJMRME), Volume II, Issue I, 2016.

Index entries for linear recurrences with constant coefficients, signature (0,46,0,-1).

Formula

a(n) = 46*a(n-2) - a(n-4) for n>4.

G.f.: x*(1 - x)*(1 + 4*x + x^2) / (1 - 46*x^2 + x^4).

Example

3 is in the sequence because (x, y) = (3, 17) is a solution to y^2 = 33*x^2 - 8.

Mathematica

LinearRecurrence[{0, 46, 0, -1}, {1, 3, 43, 137}, 30] (* Harvey P. Dale, Mar 22 2022 *)

Prog

(PARI) Vec(x*(1 - x)*(1 + 4*x + x^2) / (1 - 46*x^2 + x^4) + O(x^30))

Crossrefs

Cf. A281504.

Sequence in context: A062647 A003525 A042661 * A030990 A306970 A054698

Adjacent sequences: A281500 A281501 A281502 * A281504 A281505 A281506

Keyword

nonn,easy

Author

Colin Barker, Jan 23 2017

Status

approved