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A237255 Values of x in the solutions to x^2 - 5xy + y^2 + 17 = 0, where 0 < x < y. 3

%I #11 Jun 13 2015 00:54:58

%S 2,3,7,13,33,62,158,297,757,1423,3627,6818,17378,32667,83263,156517,

%T 398937,749918,1911422,3593073,9158173,17215447,43879443,82484162,

%U 210239042,395205363,1007315767,1893542653,4826339793,9072507902,23124383198,43468996857

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

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

%H Colin Barker, <a href="/A237255/b237255.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-1).

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

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

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

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

%Y Cf. A004253, A237254.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Feb 05 2014

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)