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A280761 Solutions y_n to the negative Pell equation y^2 = 72*x^2 - 8.

%I A280761 #37 Sep 08 2022 08:46:18
%S A280761 8,280,9512,323128,10976840,372889432,12667263848,430314081400,
%T A280761 14618011503752,496582077046168,16869172608065960,573055286597196472,
%U A280761 19467010571696614088,661305304151087682520,22464913330565284591592,763145747935068588431608
%N A280761 Solutions y_n to the negative Pell equation y^2 = 72*x^2 - 8.
%C A280761 Although this is a list, it has offset zero because one of the references numbered the solutions starting at 0.
%H A280761 Seiichi Manyama, <a href="/A280761/b280761.txt">Table of n, a(n) for n = 0..652</a>
%H A280761 S. Vidhyalakshmi, V. Krithika, K. Agalya, <a href="http://www.ijeter.everscience.org/Manuscripts/Volume-4/Issue-2/Vol-4-issue-2-M-04.pdf">On The Negative Pell Equation  y^2 = 72*x^2 - 8</a>, International Journal of Emerging Technologies in Engineering Research (IJETER), Volume 4, Issue 2, February (2016).
%H A280761 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (34,-1).
%F A280761 G.f.: 8*(1 + x)/(1 - 34*x + x^2). - _Ilya Gutkovskiy_, Jan 17 2017
%F A280761 a(n) = 34*a(n-1) - a(n-2), a(0)=8, a(1)=280. - _Seiichi Manyama_, Jan 17 2017
%F A280761 a(n) = (17+12*sqrt(2))^(-n)*(-4-3*sqrt(2) + (-4+3*sqrt(2))*(17+12*sqrt(2))^(2*n)) for n>0. - _Colin Barker_, Jan 17 2017
%t A280761 LinearRecurrence[{34, -1}, {8, 280}, 20] (* _Vincenzo Librandi_, Jan 18 2017 *)
%o A280761 (PARI) a(n)=([0,1;-1,34]^n*[-8;8])[1,1] \\ _Charles R Greathouse IV_, Jan 17 2017
%o A280761 (Magma) I:=[8,280]; [n le 2 select I[n] else 34*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Jan 18 2017
%Y A280761 For the x_n values see A077420.
%K A280761 nonn,easy
%O A280761 0,1
%A A280761 _N. J. A. Sloane_, Jan 16 2017
%E A280761 More terms from _Ilya Gutkovskiy_, Jan 17 2017