login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A084844 Denominators of the continued fraction n + 1/(n + 1/...) [n times]. 11
1, 2, 10, 72, 701, 8658, 129949, 2298912, 46866034, 1082120050, 27916772489, 795910114440, 24851643870041, 843458630403298, 30918112619119426, 1217359297034666112, 51240457936070359069, 2296067756927144738850, 109127748348241605689981 (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. - T. D. Noe, Aug 19 2004

LINKS

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

Eric Weisstein's World of Mathematics, Lucas Sequence

FORMULA

a(n) = (s^n - (-s)^(-n))/(2*s - n), where s = (n + sqrt(n^2 + 4))/2. - Vladimir Reshetnikov, May 07 2016

a(n) = y(n,n), where y(m+2,n) = n*y(m+1,n) + y(m,n), with y(0,n)=0, y(1,n)=1 for all n. - Benedict W. J. Irwin, Nov 03 2016

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

a(n) = A117715(n,n). - Bobby Jacobs, Aug 12 2017

a(n) = [x^n] x/(1 - n*x - x^2). - Ilya Gutkovskiy, Oct 10 2017

EXAMPLE

a(4) = 72 since 4 + 1/(4 + 1/(4 + 1/4)) = 305/72.

MAPLE

with(combinat): a:=proc(n) fibonacci(n, n) end: seq(a(n), n=1..30); # Zerinvary Lajos, Jan 03 2007

MATHEMATICA

myList[n_] := Module[{ex = {n}}, Do[ex = {ex, n}, {n - 1}]; Flatten[ex]] Table[Denominator[FromContinuedFraction[myList[n]]], {n, 1, 20}]

Table[s=n; Do[s=n+1/s, {n-1}]; Denominator[s], {n, 20}] (* T. D. Noe, Aug 19 2004 *)

Table[Fibonacci[n, n], {n, 1, 20}] (* Vladimir Reshetnikov, May 07 2016 *)

Table[DifferenceRoot[Function[{y, m}, {y[2+m]==n*y[1+m]+y[m], y[0]==0, y[1]==1}]][n], {n, 1, 20}] (* Benedict W. J. Irwin, Nov 03 2016 *)

PROG

(Python)

from sympy import fibonacci

def a(n): return fibonacci(n, n)

print map(a, xrange(1, 31)) # Indranil Ghosh, Aug 12 2017

CROSSREFS

Cf. A084845 (numerators).

Cf. A000045, A097690, A097691, A117715, A290864 (primes in this sequence).

Sequence in context: A185183 A052555 A204808 * A144011 A238085 A277502

Adjacent sequences:  A084841 A084842 A084843 * A084845 A084846 A084847

KEYWORD

frac,nonn

AUTHOR

Hollie L. Buchanan II, Jun 08 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 20 05:43 EDT 2019. Contains 325168 sequences. (Running on oeis4.)