The Leonardo numbers are defined by the recurrence
relation
for 
.
They begin 1, 1, 3, 5, 9, 15, 25, 41, ... (OEIS A001595).
In terms of the Fibonacci numbers,
 |
(3)
|
The sequence was named by Dijkstra (1981) and was used in his sorting
algorithm smoothsort (Dijkstra 1982).
See also
Fibonacci Number,
Integer
Sequence
Explore with Wolfram|Alpha
References
Catarino, P. M. M. C. and Borges, A. "On Leonardo Numbers." Acta Math. Univ. Comenianae 89, No. 1,
75-86, 2019. https://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1005/799.Dijkstra,
E. W. "Fibonacci Numbers and Leonardo Numbers." EWD797, July 1981.
https://www.cs.utexas.edu/users/EWD/ewd07xx/EWD797.PDF.Dijkstra,
E. W. "Smoothsort, an Alternative for Sorting in Situ." Sci. Comput.
Programming 1, 223-233, 1982. https://www.cs.utexas.edu/users/EWD/ewd07xx/EWD796a.PDF.Sloane,
N. J. A. Sequence A001595 in "The
On-Line Encyclopedia of Integer Sequences."
Cite this as:
Weisstein, Eric W. "Leonardo Number."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LeonardoNumber.html
Subject classifications
