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A106257 Numbers k such that k^2 = 12*n^2 + 13.

%I A106257 #15 Oct 21 2021 18:51:04
%S A106257 5,11,59,149,821,2075,11435,28901,159269,402539,2218331,5606645,
%T A106257 30897365,78090491,430344779,1087660229,5993929541,15149152715,
%U A106257 83484668795,211000477781,1162791433589,2938857536219,16195595401451
%N A106257 Numbers k such that k^2 = 12*n^2 + 13.
%H A106257 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,14,0,-1).
%F A106257 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 A106257 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 A106257 a(2n) = (9*A001570(n)+A001570(n+1))/2, a(2n+1) = 5*A001570(n)-6*A007655(n).
%e A106257 5^2=12*1^2+13
%e A106257 11^2=12*3^2+13
%e A106257 59^2=12*17^2+13
%e A106257 149^2=12*43^2+13
%t A106257 LinearRecurrence[{0,14,0,-1},{5,11,59,149},40] (* _Harvey P. Dale_, Oct 21 2021 *)
%o A106257 (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 A106257 Cf. A106256.
%K A106257 nonn,easy
%O A106257 1,1
%A A106257 _Pierre CAMI_, Apr 28 2005
%E A106257 Edited by _Ralf Stephan_, Jun 01 2007