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%I #25 Aug 01 2015 09:52:00
%S 1,23,43,461,859,9197,17137,183479,341881,3660383,6820483,73024181,
%T 136067779,1456823237,2714535097,29063440559,54154634161,579811987943,
%U 1080378148123,11567176318301,21553408328299,230763714378077,429987788417857,4603707111243239
%N y-values in the solution to 11*x^2-10 = y^2.
%C When are both n+1 and 11*n+1 perfect squares? This problem gives the equation 11*x^2-10 = y^2.
%H Vincenzo Librandi, <a href="/A198949/b198949.txt">Table of n, a(n) for n = 1..250</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 20, 0, -1).
%F a(n+4) = 20*a(n+2)-a(n) with a(1)=1, a(2)=23, a(3)=43, a(4)=461.
%F G.f.: x*(1+x)*(1+22*x+x^2)/(1-20*x^2+x^4). - _Bruno Berselli_, Nov 04 2011
%F a(n) = ((-(-1)^n-t)*(10-3*t)^floor(n/2)+(-(-1)^n+t)*(10+3*t)^floor(n/2))/2 where t=sqrt(11). - _Bruno Berselli_, Nov 14 2011
%t LinearRecurrence[{0, 20, 0, -1}, {1,23,43,461}, 24] (* _Bruno Berselli_, Nov 11 2011 *)
%o (Maxima) makelist(expand(((-(-1)^n-sqrt(11))*(10-3*sqrt(11))^floor(n/2)+(-(-1)^n+sqrt(11))*(10+3*sqrt(11))^floor(n/2))/2), n, 1, 24); /* _Bruno Berselli_, Nov 14 2011 */
%Y Cf. A198947.
%K nonn,easy
%O 1,2
%A _Sture Sjöstedt_, Oct 31 2011
%E More terms from _Bruno Berselli_, Nov 04 2011
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