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%I #11 Jul 10 2019 16:30:11
%S 0,288,960,1632,2688,6048,9792,15840,35328,57120,92352,205920,332928,
%T 538272,1200192,1940448,3137280,6995232,11309760,18285408,40771200,
%U 65918112,106575168,237631968,384198912,621165600,1385020608,2239275360,3620418432,8072491680
%N Solutions y to the negative Pell equation y^2 = 72*x^2 - 332928 with x,y >= 0.
%C The corresponding values of x are in A281235.
%H Colin Barker, <a href="/A281236/b281236.txt">Table of n, a(n) for n = 1..1000</a>
%H 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 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,6,0,0,-1).
%F a(n) = 6*a(n-3) - a(n-6) for n>6.
%F G.f.: 96*x^2*(3 + 10*x + 17*x^2 + 10*x^3 + 3*x^4) / (1 - 6*x^3 + x^6).
%e 288 is in the sequence because (x, y) = (76, 288) is a solution to y^2 = 72*x^2 - 332928.
%t LinearRecurrence[{0,0,6,0,0,-1},{0,288,960,1632,2688,6048},30] (* _Harvey P. Dale_, Jul 10 2019 *)
%o (PARI) concat(0, Vec(96*x^2*(3 + 10*x + 17*x^2 + 10*x^3 + 3*x^4) / (1 - 6*x^3 + x^6) + O(x^40)))
%Y Cf. A281235.
%Y Equals 2*A281240.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 19 2017