Author:
Liptai Kálmán,Szalay László
Abstract
AbstractLet $$G_0=0$$
G
0
=
0
and $$G_1=1$$
G
1
=
1
. The present study deals with the inhomogeneous version $$\begin{aligned} G_n=G_{n-1}+G_{n-2}+w_{n-2} \end{aligned}$$
G
n
=
G
n
-
1
+
G
n
-
2
+
w
n
-
2
of the Fibonacci sequence, where $$w_{n-2}$$
w
n
-
2
takes value a with probability p, and does value b with $$1-p$$
1
-
p
. We describe the probability distribution of the values of $$G_n$$
G
n
with fixed n, and examine the properties like expected value and variance. The most challenging feature is the fractal-like structure of the distribution.
Funder
Hungarian Scientific Research Fund
VEGA
University of Sopron
Publisher
Springer Science and Business Media LLC
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