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

0,2

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).

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]

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 *)

Crossrefs

Cf. A010507, A041092.

Sequence in context: A279180 A279471 A042265 * A154746 A042781 A308885

Adjacent sequences: A041090 A041091 A041092 * A041094 A041095 A041096

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved