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A106256 Numbers n such that 12*n^2 + 13 is a square. 2

%I

%S 1,3,17,43,237,599,3301,8343,45977,116203,640377,1618499,8919301,

%T 22542783,124229837,313980463,1730298417,4373183699,24099948001,

%U 60910591323,335668973597,848375094823,4675265682357,11816340736199

%N Numbers n such that 12*n^2 + 13 is a square.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,14,0,-1).

%F Recurrence: a(1)=1, a(2)=3, a(3)=14*a(1)+a(2), a(4)=14*a(2)+a(1) then a(n)=14*a(n-2)-a(n-4).

%F G.f.: x*(x+1)^3 / ((x^2-4*x+1)*(x^2+4*x+1)). - Corrected by _Colin Barker_, Apr 16 2014

%F a(2n) = 4*A007655(n)-A001570(n-1), a(2n+1) = 4*A007655(n)+A001570(n).

%e 12*1^2+13 = 5^2.

%e 12*3^2+13 = 11^2.

%e 12*17^2+13 = 59^2.

%o (PARI) Vec(x*(x+1)^3/((x^2-4*x+1)*(x^2+4*x+1)) + O(x^100)) \\ _Colin Barker_, Apr 16 2014

%Y Cf. A106257.

%K nonn,easy

%O 1,2

%A _Pierre CAMI_, Apr 28 2005

%E Edited by _Ralf Stephan_, Jun 01 2007

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Last modified May 18 00:43 EDT 2021. Contains 343992 sequences. (Running on oeis4.)