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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• frac

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).

Crossrefs

Cf. A041118, A040059, A020825, A010520.

Programs

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

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 *)

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

Extensions

More terms from Colin Barker, Nov 13 2013