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Solutions x to the negative Pell equation y^2 = 72*x^2 - 83232 with x,y >= 0.
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%I #8 Jan 19 2017 12:52:01

%S 34,38,66,102,162,358,578,934,2082,3366,5442,12134,19618,31718,70722,

%T 114342,184866,412198,666434,1077478,2402466,3884262,6280002,14002598,

%U 22639138,36602534,81613122,131950566,213335202,475676134,769064258,1243408678,2772443682

%N Solutions x to the negative Pell equation y^2 = 72*x^2 - 83232 with x,y >= 0.

%C The corresponding values of y are in A281240.

%H Colin Barker, <a href="/A281239/b281239.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.: 2*x*(17 + 19*x + 33*x^2 - 51*x^3 - 33*x^4 - 19*x^5) / (1 - 6*x^3 + x^6).

%e 38 is in the sequence because (x, y) = (38,144) is a solution to y^2 = 72*x^2 - 83232.

%o (PARI) Vec(2*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. A281240.

%Y Equals (1/4)* A281241.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Jan 19 2017