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A041027 Denominators of continued fraction convergents to sqrt(18). 5
1, 4, 33, 136, 1121, 4620, 38081, 156944, 1293633, 5331476, 43945441, 181113240, 1492851361, 6152518684, 50713000833, 209004522016, 1722749176961, 7100001229860, 58522759015841, 241191037293224 (list; graph; refs; listen; history; text; internal format)
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 *)

CROSSREFS

Cf. A010474, A041026.

Sequence in context: A297515 A027169 A152041 * A209034 A095671 A278671

Adjacent sequences:  A041024 A041025 A041026 * A041028 A041029 A041030

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 16 17:39 EST 2018. Contains 317275 sequences. (Running on oeis4.)