Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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