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%I #24 Mar 15 2023 14:02:46
%S 1,4,7,43,76,469,829,5116,9043,55807,98644,608761,1076041,6640564,
%T 11737807,72437443,128039836,790171309,1396700389,8619446956,
%U 15235664443,94023745207,166195608484,1025641750321,1812916028881,11188035508324,19775880709207
%N x-values in the solution to 13*x^2 - 12 = y^2.
%C When are both n+1 and 13*n+1 perfect squares? This problem gives the equation 13*x^2-12=y^2.
%H Vincenzo Librandi, <a href="/A199404/b199404.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 (0,11,0,-1).
%F a(n+4) = 11*a(n+2)-a(n) with a(1)=1, a(2)=4, a(3)=7, a(4)=43.
%F G.f.: x*(1-x)*(1+5*x+x^2)/(1-11*x^2+x^4). - _Bruno Berselli_, Nov 08 2011
%t LinearRecurrence[{0, 11, 0, -1}, {1, 4, 7, 43}, 50] (* _T. D. Noe_, Nov 07 2011 *)
%o (Magma) m:=28; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1-x)*(1+5*x+x^2)/(1-11*x^2+x^4))); // _Bruno Berselli_, Nov 08 2011
%Y Cf. A199405.
%K nonn,easy
%O 1,2
%A _Sture Sjöstedt_, Nov 05 2011
%E More terms from _T. D. Noe_, Nov 07 2011
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