Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Jan 25 2017 10:04:27
%S 0,48,288,1680,9792,57072,332640,1938768,11299968,65861040,383866272,
%T 2237336592,13040153280,76003583088,442981345248,2581884488400,
%U 15048325585152,87708069022512,511200088549920,2979492462277008,17365754685112128,101215035648395760
%N Solutions y to the negative Pell equation y^2 = 72*x^2 - 288 with x,y >= 0.
%C The corresponding values of x are in A003499.
%H Colin Barker, <a href="/A281234/b281234.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_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).
%F G.f.: 48*x^2 / (1 - 6*x + x^2).
%F a(n) = 6*a(n-1) - a(n-2) for n>2.
%F a(n) = 48*A001109(n-1).
%F a(n) = 6*sqrt(2)*(-(3 - 2*sqrt(2))^n*(3+2*sqrt(2)) + (3 - 2*sqrt(2))*(3 + 2*sqrt(2))^n).
%e 48 is in the sequence because (x, y) = (6,48) is a solution to y^2 = 72*x^2 - 288.
%o (PARI) concat(0, Vec(48*x^2 / (1 - 6*x + x^2) + O(x^25)))
%Y Cf. A001109, A003499, A077420, A280761.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Jan 18 2017