A237255 Values of x in the solutions to x^2 - 5xy + y^2 + 17 = 0, where 0 < x < y.

2, 3, 7, 13, 33, 62, 158, 297, 757, 1423, 3627, 6818, 17378, 32667, 83263, 156517, 398937, 749918, 1911422, 3593073, 9158173, 17215447, 43879443, 82484162, 210239042, 395205363, 1007315767, 1893542653, 4826339793, 9072507902, 23124383198, 43468996857

Offset

1,1

Comments

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

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,5,0,-1).

Formula

a(n) = 5*a(n-2)-a(n-4).

G.f.: -x*(x-1)*(x+2)*(2*x+1) / (x^4-5*x^2+1).

Example

3 is in the sequence because (x, y) = (3, 13) is a solution to x^2 - 5xy + y^2 + 17 = 0.

Prog

(PARI) Vec(-x*(x-1)*(x+2)*(2*x+1)/(x^4-5*x^2+1) + O(x^100))

Crossrefs

Cf. A004253, A237254.

Sequence in context: A007827 A250308 A259145 * A129859 A280765 A056953

Adjacent sequences: A237252 A237253 A237254 * A237256 A237257 A237258

Keyword

nonn,easy

Author

Colin Barker, Feb 05 2014

Status

approved