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A097691 Denominators of the continued fraction n-1/(n-1/...) [n times]. 4
1, 2, 8, 56, 551, 6930, 105937, 1905632, 39424240, 922080050, 24057287759, 692686638072, 21817946138353, 746243766783074, 27543862067299424, 1091228270370045824, 46187969968474139807, 2080128468827570457762, 99318726126650358502921, 5011361251329169946919800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The (n-1)-th term of the Lucas sequence U(n,1). The numerator is the n-th term. Adjacent terms of the sequence U(n,1) are relatively prime.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..387

Eric Weisstein's World of Mathematics, Lucas Sequence

FORMULA

a(n) = ChebyshevU(n-1,n/2). - Gary Detlefs, Oct 15 2011

a(n) = abs((2^(-n) * (sqrt(4 - n^2) + i*n)^n - 2^n*(-sqrt(4 - n^2) - i*n)^(-n))/sqrt(4 - n^2)), where i is the imaginary unit, for n > 2. - Daniel Suteu, May 31 2017

a(n) ~ n^(n-1). - Vaclav Kotesovec, Jun 03 2017

EXAMPLE

a(4) = 56 because 4-1/(4-1/(4-1/4)) = 209/56.

MATHEMATICA

Table[s=n; Do[s=n-1/s, {n-1}]; Denominator[s], {n, 20}]

Table[Abs[Fibonacci[n, I n]], {n, 20}] (* Vladimir Reshetnikov, Oct 16 2018 *)

PROG

(Sage) [lucas_number1(n, n, 1) for n in range(1, 19)] # Zerinvary Lajos, Jul 16 2008

CROSSREFS

Cf. A084844, A084845, A097690 (numerators).

Sequence in context: A109618 A201128 A277498 * A181939 A124212 A326009

Adjacent sequences:  A097688 A097689 A097690 * A097692 A097693 A097694

KEYWORD

easy,frac,nonn

AUTHOR

T. D. Noe, Aug 19 2004

STATUS

approved

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Last modified August 3 08:53 EDT 2020. Contains 336197 sequences. (Running on oeis4.)