%I #15 Oct 21 2021 18:51:04
%S 5,11,59,149,821,2075,11435,28901,159269,402539,2218331,5606645,
%T 30897365,78090491,430344779,1087660229,5993929541,15149152715,
%U 83484668795,211000477781,1162791433589,2938857536219,16195595401451
%N Numbers k such that k^2 = 12*n^2 + 13.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,14,0,-1).
%F k(1)=5, k(2)=11, k(3)=14*k(1)-k(2), k(4)=14*k(2)-k(1) then k(n)=14*k(n-2)-k(n-4).
%F G.f.: -x*(x-1)*(5*x^2+16*x+5) / ((x^2-4*x+1)*(x^2+4*x+1)). - Corrected by _Colin Barker_, Apr 16 2014
%F a(2n) = (9*A001570(n)+A001570(n+1))/2, a(2n+1) = 5*A001570(n)-6*A007655(n).
%e 5^2=12*1^2+13
%e 11^2=12*3^2+13
%e 59^2=12*17^2+13
%e 149^2=12*43^2+13
%t LinearRecurrence[{0,14,0,-1},{5,11,59,149},40] (* _Harvey P. Dale_, Oct 21 2021 *)
%o (PARI) Vec(-x*(x-1)*(5*x^2+16*x+5)/((x^2-4*x+1)*(x^2+4*x+1)) + O(x^100)) \\ _Colin Barker_, Apr 16 2014
%Y Cf. A106256.
%K nonn,easy
%O 1,1
%A _Pierre CAMI_, Apr 28 2005
%E Edited by _Ralf Stephan_, Jun 01 2007