%I #13 Nov 05 2022 20:00:09
%S 0,2,52,1350,35048,909898,23622300,613269902,15921395152,413343004050,
%T 10730996710148,278592571459798,7232675861244600,187770979820899802,
%U 4874812799482150252,126557361806715006750,3285616594175108025248
%N y-values in the solution to x^2 - 42*y^2 = 1.
%C The corresponding values of x of this Pell equation are in A097308.
%H Vincenzo Librandi, <a href="/A174779/b174779.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (26,-1).
%F a(n) = 26*a(n-1)-a(n-2) with a(1)=0, a(2)=2.
%F G.f.: 2*x^2/(1-26*x+x^2).
%t LinearRecurrence[{26,-1},{0,2},30]
%t With[{c=2*Sqrt[42]},Table[-((13-c)^n-(13+c)^n)/c,{n,0,20}]]//Simplify (* _Harvey P. Dale_, Nov 05 2022 *)
%o (Magma) I:=[0, 2]; [n le 2 select I[n] else 26*Self(n-1)-Self(n-2): n in [1..20]];
%Y Cf. A097308.
%K nonn,easy
%O 1,2
%A _Vincenzo Librandi_, Apr 15 2010