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%I #14 Mar 22 2022 18:38:23
%S 1,3,43,137,1977,6299,90899,289617,4179377,13316083,192160443,
%T 612250201,8835201001,28150193163,406227085603,1294296635297,
%U 18677610736737,59509495030499,858763866804299,2736142474767657,39484460262261017,125803044344281723
%N Solutions x to the negative Pell equation y^2 = 33*x^2 - 8 with x,y >= 0.
%H Colin Barker, <a href="/A281503/b281503.txt">Table of n, a(n) for n = 1..1000</a>
%H M. A. Gopalan, S. Vidhyalakshmi, E. Premalatha, R. Janani, <a href="http://rdmodernresearch.org/wp-content/uploads/2016/02/143.pdf">On The Negative Pell Equation y^2 = 33*x^2 - 8</a>, International Journal of Multidisciplinary Research and Modern Education (IJMRME), Volume II, Issue I, 2016.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,46,0,-1).
%F a(n) = 46*a(n-2) - a(n-4) for n>4.
%F G.f.: x*(1 - x)*(1 + 4*x + x^2) / (1 - 46*x^2 + x^4).
%e 3 is in the sequence because (x, y) = (3, 17) is a solution to y^2 = 33*x^2 - 8.
%t LinearRecurrence[{0,46,0,-1},{1,3,43,137},30] (* _Harvey P. Dale_, Mar 22 2022 *)
%o (PARI) Vec(x*(1 - x)*(1 + 4*x + x^2) / (1 - 46*x^2 + x^4) + O(x^30))
%Y Cf. A281504.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 23 2017
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