A237262 Values of x in the solutions to x^2 - 8*x*y + y^2 + 11 = 0, where 0 < x < y.

1, 2, 6, 15, 47, 118, 370, 929, 2913, 7314, 22934, 57583, 180559, 453350, 1421538, 3569217, 11191745, 28100386, 88112422, 221233871, 693707631, 1741770582, 5461548626, 13712930785, 42998681377, 107961675698, 338527902390, 849980474799, 2665224537743

Offset

1,2

Comments

The corresponding values of y are given by a(n+2).

Also values of y in the solutions to the negative Pell equation x^2 - 15*y^2 = -11. - Colin Barker, Jan 25 2017

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,8,0,-1).

Formula

G.f.: -x*(x-1)*(x^2 + 3*x + 1) / (x^4 - 8*x^2 + 1).

a(n) = 8*a(n-2) - a(n-4) for n > 4.

a(n) = (11*a(n-1) - 4*a(n-2))/3 if n is odd; a(n) = (11*a(n-1) - 3*a(n-2))/4 if n is even. - R. J. Mathar, Jun 18 2014

Example

6 is a term because (x, y) = (6, 47) is a solution to x^2 - 8xy + y^2 + 11 = 0.

Mathematica

LinearRecurrence[{0, 8, 0, -1}, {1, 2, 6, 15}, 30] (* Harvey P. Dale, Sep 06 2020 *)

Prog

(PARI) Vec(-x*(x-1)*(x^2+3*x+1)/(x^4-8*x^2+1) + O(x^100))

Crossrefs

Cf. A001091, A070997, A199336, A281584.

For first and second differences see A322780, A199336.

Sequence in context: A045628 A186738 A127383 * A291848 A363207 A196961

Adjacent sequences: A237259 A237260 A237261 * A237263 A237264 A237265

Keyword

nonn,easy

Author

Colin Barker, Feb 05 2014

Status

approved