A041119 Denominators of continued fraction convergents to sqrt(68).

1, 4, 65, 264, 4289, 17420, 283009, 1149456, 18674305, 75846676, 1232221121, 5004731160, 81307919681, 330236409884, 5365090477825, 21790598321184, 354014663616769, 1437849252788260, 23359602708228929, 94876260085703976, 1541379764079492545

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,66,0,-1).

Formula

G.f.: -(x^2-4*x-1) / ((x^2-8*x-1)*(x^2+8*x-1)). - Colin Barker, Nov 13 2013

a(n) = 66*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[68], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
Denominator[Convergents[Sqrt[68], 30]] (* Vincenzo Librandi, Dec 11 2013 *)

Prog

(Magma) I:=[1, 4, 65, 264]; [n le 4 select I[n] else 66*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041118, A040059, A020825, A010520.

Sequence in context: A119601 A058438 A171959 * A278547 A293562 A331577

Adjacent sequences: A041116 A041117 A041118 * A041120 A041121 A041122

Keyword

nonn,cofr,easy,frac

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 13 2013

Status

approved