A041093 Denominators of continued fraction convergents to sqrt(54).

1, 2, 3, 20, 23, 66, 947, 1960, 2907, 19402, 22309, 64020, 918589, 1901198, 2819787, 18819920, 21639707, 62099334, 891030383, 1844160100, 2735190483, 18255302998, 20990493481, 60236289960, 864298552921, 1788833395802, 2653131948723, 17707625088140

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,970,0,0,0,0,0,-1).

Crossrefs

Cf. A010507, A041092.

Programs

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[54], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)
Denominator[Convergents[Sqrt[54], 30]] (* Vincenzo Librandi, Oct 24 2013 *)

Formula

a(n) = 970*a(n-6)-a(n-12). G.f.: -(x^10-2*x^9+3*x^8-20*x^7+23*x^6-66*x^5-23*x^4-20*x^3-3*x^2-2*x-1)/((x^4-10*x^2+1)*(x^8+10*x^6+99*x^4+10*x^2+1)). [Colin Barker, Jul 18 2012]