This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000301 a(n) = a(n-1)*a(n-2) with a(0) = 1, a(1) = 2; also a(n) = 2^Fibonacci(n). 39
 1, 2, 2, 4, 8, 32, 256, 8192, 2097152, 17179869184, 36028797018963968, 618970019642690137449562112, 22300745198530623141535718272648361505980416, 13803492693581127574869511724554050904902217944340773110325048447598592 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Continued fraction expansion of s = 1.709803442861291... = Sum_{k >= 0} (1/2^floor(k * phi)) where phi is the golden ratio (1 + sqrt(5))/2. - Benoit Cloitre, Aug 19 2002 a(n) = A000304(n+3) / A010098(n+1). - Reinhard Zumkeller, Jul 06 2014 The continued fraction expansion of the above constant s is [1; 1, 2, 2, 4, ...], that of the rabbit constant r = s-1 = A014565 is [0; 1, 2, 2, 4, ...]. - M. F. Hasler, Nov 10 2018 REFERENCES Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002, p. 913. LINKS T. D. Noe, Table of n, a(n) for n = 0..18 J. L. Davison, A series and its associated continued fraction, Proc. Amer. Math. Soc., 63 (1977), 29-32. Samuele Giraudo, Intervals of balanced binary trees in the Tamari lattice, arXiv preprint arXiv:1107.3472 (2011). FORMULA a(n) ~ k^phi^n with k = 2^(1/sqrt(5)) = 1.3634044... and phi the golden ratio. - Charles R Greathouse IV, Jan 12 2012 MAPLE A000301 := proc(n) option remember; if n <=2 then n else A000301(n-1)*A000301(n-2); fi; end: seq(A000301(n), n=1..15); MATHEMATICA 2^Fibonacci[Range[0, 14]] (* Alonso del Arte, Jul 28 2016 *) PROG (MAGMA) [2^Fibonacci(n): n in [0..20]]; // Vincenzo Librandi, Apr 18 2011 (PARI) a(n)=1<

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.

Last modified December 11 13:08 EST 2018. Contains 318049 sequences. (Running on oeis4.)