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Solutions y to the negative Pell equation y^2 = 33*x^2 - 8 with x,y >= 0.
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%I #9 Sep 06 2023 13:48:17

%S 5,17,247,787,11357,36185,522175,1663723,24008693,76495073,1103877703,

%T 3517109635,50754365645,161710548137,2333596941967,7435168104667,

%U 107294704964837,341856022266545,4933222831440535,15717941856156403,226820955541299773,722683469360927993

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

%H Colin Barker, <a href="/A281504/b281504.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)*(5 + 12*x + 5*x^2) / (1 - 46*x^2 + x^4).

%e 17 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},{5,17,247,787},30] (* _Harvey P. Dale_, Sep 06 2023 *)

%o (PARI) Vec(x*(1 + x)*(5 + 12*x + 5*x^2) / (1 - 46*x^2 + x^4) + O(x^30))

%Y Cf. A281503.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Jan 23 2017