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

5, 11, 59, 149, 821, 2075, 11435, 28901, 159269, 402539, 2218331, 5606645, 30897365, 78090491, 430344779, 1087660229, 5993929541, 15149152715, 83484668795, 211000477781, 1162791433589, 2938857536219, 16195595401451

Offset: 1

Author

Pierre CAMI, Apr 28 2005

Keywords

• nonn
• easy

Examples

			5^2=12*1^2+13
11^2=12*3^2+13
59^2=12*17^2+13
149^2=12*43^2+13
		

Links

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

Crossrefs

Cf. A106256.

Programs

Mathematica

LinearRecurrence[{0,14,0,-1},{5,11,59,149},40] (* Harvey P. Dale, Oct 21 2021 *)

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

Formula

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).

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

a(2n) = (9*A001570(n)+A001570(n+1))/2, a(2n+1) = 5*A001570(n)-6*A007655(n).

Extensions

Edited by Ralf Stephan, Jun 01 2007