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%I #24 Sep 08 2022 08:46:18
%S 2,7,23,58,182,457,1433,3598,11282,28327,88823,223018,699302,1755817,
%T 5505593,13823518,43345442,108832327,341257943,856835098,2686718102,
%U 6745848457,21152486873,53109952558,166533176882,418133772007,1311112928183,3291960223498
%N Solutions x to the negative Pell equation x^2 - 15*y^2 = -11 with x, y > 0.
%C The corresponding values of y are in A237262.
%H Colin Barker, <a href="/A281584/b281584.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-1).
%F G.f.: x*(1 + x)*(2 + x)*(1 + 2*x) / (1 - 8*x^2 + x^4).
%F a(n) = 8*a(n-2) - a(n-4) for n>4.
%F From _Bruno Berselli_, Jan 25 2017: (Start)
%F a(n) = (11*a(n-1) - 4*a(n-2))/3 if n is odd, a(n) = (11*a(n-1) - 3*a(n-2))/4 if n is even (see also _R. J. Mathar_ in A237262).
%F a(n)*a(n-3) - a(n-1)*a(n-2) = -15*(7-(-1)^n)/2, with n>3. Example: for n=8, a(8)*a(5) - a(7)*a(6) = 3598*182 - 1433*457 = -15*3. (End)
%e 7 is in the sequence because (x, y) = (7, 2) is a solution to x^2 - 15*y^2 = -11.
%t LinearRecurrence[{0, 8, 0, -1}, {2, 7, 23, 58}, 30] (* _Bruno Berselli_, Jan 25 2017 *)
%o (PARI) Vec(x*(1 + x)*(2 + x)*(1 + 2*x) / (1 - 8*x^2 + x^4) + O(x^30))
%o (Magma) [n le 2 select 5*n-3 else IsOdd(n) select (11*Self(n-1)-4*Self(n-2))/3 else (11*Self(n-1)-3*Self(n-2))/4: n in [1..30]]; // _Bruno Berselli_, Jan 25 2017
%Y Cf. A237262.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Jan 25 2017
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