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

1,1

Links

Table of n, a(n) for n=1..30.

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A133301.

Sequence in context: A330582 A104258 A143904 * A173746 A095803 A036345

Adjacent sequences: A144794 A144795 A144796 * A144798 A144799 A144800

Keyword

nonn,easy

Author

Richard Choulet, Sep 21 2008

Extensions

Corrected by R. J. Mathar, Nov 27 2011

Editing and more terms from Colin Barker, Oct 20 2014

Status

approved