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%I #20 Feb 11 2024 04:20:09
%S 11,15,24,41,80,141,249,440,869,1536,2715,4799,9479,16755,29616,52349,
%T 103400,182769,323061,571040,1127921,1993704,3524055,6229091,12303731,
%U 21747975,38441544,67948961,134213120,237234021,419332929,741209480,1464040589
%N x-values in the solution to x^2 - 13y^2 = 108.
%C This equation is used for worked examples in the Robertson link.
%H Vincenzo Librandi, <a href="/A228205/b228205.txt">Table of n, a(n) for n = 1..1000</a>
%H John P. Robertson, <a href="https://web.archive.org/web/20180831180333/http://www.jpr2718.org/pell.pdf">Solving the generalized Pell equation x^2 - Dy^2 = N</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,11,0,0,0,-1).
%F G.f.: -x*(x-1)*(11*x^6+26*x^5+50*x^4+91*x^3+50*x^2+26*x+11) / ((x^4-3*x^2-1)*(x^4+3*x^2-1)).
%F a(n) = 11*a(n-4)-a(n-8).
%t CoefficientList[Series[-(x - 1) (11 x^6 + 26 x^5 + 50 x^4 + 91 x^3 + 50 x^2 + 26 x + 11) / ((x^4 - 3 x^2 - 1) (x^4 + 3 x^2 - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 17 2013 *)
%o (PARI) Vec(-x*(x-1)*(11*x^6+26*x^5+50*x^4+91*x^3+50*x^2+26*x+11)/((x^4-3*x^2-1)*(x^4+3*x^2-1)) + O(x^100))
%Y Cf. A228206.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Aug 16 2013
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