%I #11 Jan 19 2017 12:51:51
%S 136,152,264,408,648,1432,2312,3736,8328,13464,21768,48536,78472,
%T 126872,282888,457368,739464,1648792,2665736,4309912,9609864,15537048,
%U 25120008,56010392,90556552,146410136,326452488,527802264,853340808,1902704536,3076257032
%N Solutions x to the negative Pell equation y^2 = 72*x^2 - 1331712 with x,y >= 0.
%C The corresponding values of y are in A281242.
%H Colin Barker, <a href="/A281241/b281241.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.: 8*x*(17 + 19*x + 33*x^2 - 51*x^3 - 33*x^4 - 19*x^5) / (1 - 6*x^3 + x^6).
%e 152 is in the sequence because (x, y) = (152,576) is a solution to y^2 = 72*x^2 - 1331712.
%t Rest@ CoefficientList[Series[8 x (17 + 19 x + 33 x^2 - 51 x^3 - 33 x^4 - 19 x^5)/(1 - 6 x^3 + x^6), {x, 0, 31}], x] (* _Michael De Vlieger_, Jan 19 2017 *)
%o (PARI) Vec(8*x*(17 + 19*x + 33*x^2 - 51*x^3 - 33*x^4 - 19*x^5) / (1 - 6*x^3 + x^6) + O(x^40))
%Y Cf. A281242.
%Y Equals 4*A281239.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Jan 19 2017