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