A041027 Denominators of continued fraction convergents to sqrt(18).

1, 4, 33, 136, 1121, 4620, 38081, 156944, 1293633, 5331476, 43945441, 181113240, 1492851361, 6152518684, 50713000833, 209004522016, 1722749176961, 7100001229860, 58522759015841, 241191037293224

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (0,34,0,-1).

Formula

G.f.: (1+4*x-x^2)/(1-34*x^2+x^4). - Colin Barker, Jan 02 2012

From Gerry Martens, Jul 11 2015: (Start)

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

a0(n) = ((3+2*sqrt(2))/(17+12*sqrt(2))^n+(3-2*sqrt(2))*(17+12*sqrt(2))^n)/6.

a1(n) = (-1/(17+12*sqrt(2))^n+(17+12*sqrt(2))^n)/(6*sqrt(2)). (End)

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[18], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
a0[n_] := ((3+2*Sqrt[2])/(17+12*Sqrt[2])^n+(3-2*Sqrt[2])*(17+12*Sqrt[2])^n)/6 // Simplify
a1[n_] := (-1/(17+12*Sqrt[2])^n+(17+12*Sqrt[2])^n)/(6*Sqrt[2]) // Simplify
Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* Gerry Martens, Jul 11 2015 *)
LinearRecurrence[{0, 34, 0, -1}, {1, 4, 33, 136}, 20] (* Harvey P. Dale, Jan 05 2019 *)

Crossrefs

Cf. A010474, A041026.

Sequence in context: A297515 A027169 A152041 * A362820 A364946 A209034

Adjacent sequences: A041024 A041025 A041026 * A041028 A041029 A041030

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved