A144797 Numbers k such that 2*k^2 + 17 is a square.

2, 4, 16, 26, 94, 152, 548, 886, 3194, 5164, 18616, 30098, 108502, 175424, 632396, 1022446, 3685874, 5959252, 21482848, 34733066, 125211214, 202439144, 729784436, 1179901798, 4253495402, 6876971644, 24791187976, 40081928066, 144493632454, 233614596752

Offset: 1

Author

Richard Choulet, Sep 21 2008

Keywords

• nonn
• easy

Examples

			a(1)=2 because 2*4 + 17 = 25 = 5^2.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1).

Crossrefs

Cf. A133301.

Programs

Mathematica

Select[Range[6000000],IntegerQ[Sqrt[2#^2+17]]&] (* Harvey P. Dale, Aug 18 2012 *)
LinearRecurrence[{0, 6, 0, -1}, 2{1, 2, 8, 13}, 30] (* Robert G. Wilson v, Dec 02 2014 *)

PARI

Vec(2*x*(1+x)*(1+x+x^2) / ((x^2+2*x-1)*(x^2-2*x-1)) + O(x^50)) \\ Colin Barker, Oct 20 2014

Formula

G.f.: 2*x*(1+x)*(1+x+x^2) / ( (x^2+2*x-1)*(x^2-2*x-1) ). - R. J. Mathar, Nov 27 2011

a(n) = 2*A077241(n-1). - R. J. Mathar, Nov 27 2011

a(n) = 6*a(n-2) - a(n-4). - Colin Barker, Oct 20 2014

Extensions

Corrected by R. J. Mathar, Nov 27 2011

Editing and more terms from Colin Barker, Oct 20 2014