%I #28 Sep 08 2022 08:46:01
%S 2,5,37,82,590,1307,9403,20830,149858,331973,2388325,5290738,38063342,
%T 84319835,606625147,1343826622,9667939010,21416906117,154080399013,
%U 341326671250,2455618445198,5439809833883,39135814724155,86695630670878
%N x-values in the solution to x^2 - 7*y^2 = -3.
%C The corresponding values of y of this Pell equation are in A202638.
%H Bruno Berselli, <a href="/A202637/b202637.txt">Table of n, a(n) for n = 1..1000</a>
%H R. A. Mollin, <a href="http://dx.doi.org/10.1090/S0025-5718-1987-0866112-5">Class Numbers of Quadratic Fields Determinet by Solvability of Diophantine Equations</a>, Mathematics of Computation Vol. 48, 1987, p. 235 (Theorem 1.1, particular case).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,16,0,-1).
%F G.f.: x*(1+x)*(2+3*x+2*x^2)/(1-16*x^2+x^4).
%F a(n) = -a(-n+1) = ((-2*(-1)^n+sqrt(7))*(8+3*sqrt(7))^floor(n/2)-(2*(-1)^n+sqrt(7))*(8-3*sqrt(7))^floor(n/2))/2.
%F a(2n)-a(2n-1) = A202638(2n)+A202638(2n-1).
%t LinearRecurrence[{0,16,0,-1}, {2, 5, 37, 82}, 24]
%o (PARI) a=vector(24); a[1]=2; a[2]=5; a[3]=37; a[4]=82; for(i=5, #a, a[i]=16*a[i-2]-a[i-4]); a
%o (Magma) m:=24; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x)*(2+3*x+2*x^2)/(1-16*x^2+x^4)));
%o (Maxima) makelist(expand(((-2*(-1)^n+sqrt(7))*(8+3*sqrt(7))^floor(n/2)-(2*(-1)^n+sqrt(7))*(8-3*sqrt(7))^floor(n/2))/2), n, 1, 24);
%K nonn,easy
%O 1,1
%A _Bruno Berselli_, Dec 22 2011
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