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

1, 3, 17, 43, 237, 599, 3301, 8343, 45977, 116203, 640377, 1618499, 8919301, 22542783, 124229837, 313980463, 1730298417, 4373183699, 24099948001, 60910591323, 335668973597, 848375094823, 4675265682357, 11816340736199

Offset

1,2

Links

Table of n, a(n) for n=1..24.

Index entries for linear recurrences with constant coefficients, signature (0,14,0,-1).

Formula

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).

G.f.: x*(x+1)^3 / ((x^2-4*x+1)*(x^2+4*x+1)). - Corrected by Colin Barker, Apr 16 2014

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

Example

12*1^2+13 = 5^2.
12*3^2+13 = 11^2.
12*17^2+13 = 59^2.

Prog

(PARI) Vec(x*(x+1)^3/((x^2-4*x+1)*(x^2+4*x+1)) + O(x^100)) \\ Colin Barker, Apr 16 2014

Crossrefs

Cf. A106257.

Sequence in context: A215429 A126587 A108126 * A091624 A106078 A087908

Adjacent sequences: A106253 A106254 A106255 * A106257 A106258 A106259

Keyword

nonn,easy

Author

Pierre CAMI, Apr 28 2005

Extensions

Edited by Ralf Stephan, Jun 01 2007

Status

approved