A041031 Denominators of continued fraction convergents to sqrt(20).

1, 2, 17, 36, 305, 646, 5473, 11592, 98209, 208010, 1762289, 3732588, 31622993, 66978574, 567451585, 1201881744, 10182505537, 21566892818, 182717648081, 387002188980, 3278735159921, 6944472508822

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,18,0,-1).

Formula

G.f.: (1+2*x-x^2)/(1-18*x^2+x^4). - Colin Barker, Jan 01 2012

From Gerry Martens, Jul 11 2015: (Start)

Interspersion of 2 sequences [a0(n),a1(n)] for n>0:

a0(n) = ((5+2*sqrt(5))/(9+4*sqrt(5))^n+(5-2*sqrt(5))*(9+4*sqrt(5))^n)/10.

a1(n) = (-1/(9+4*sqrt(5))^n+(9+4*sqrt(5))^n)/(4*sqrt(5)). (End)

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[20], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
a0[n_] := ((5+2*Sqrt[5])/(9+4*Sqrt[5])^n+(5-2*Sqrt[5])*(9+4*Sqrt[5])^n)/10 //Simplify
a1[n_] := (-1/(9+4*Sqrt[5])^n+(9+4*Sqrt[5])^n)/(4*Sqrt[5]) //Simplify
Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* Gerry Martens, Jul 11 2015 *)

Crossrefs

Cf. A010476, A041030.

Sequence in context: A342485 A342487 A342613 * A041965 A095075 A307161

Adjacent sequences: A041028 A041029 A041030 * A041032 A041033 A041034

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved