Hexanacci Number
The hexanacci numbers are a generalization of the Fibonacci numbers defined by 
, 
, 
, 
, 
, 
, and the recurrence
relation
 |
(1)
|
for 
. They represent the 
case of the
Fibonacci n-step numbers.
The first few terms for 
, 2, ... are
1, 1, 2, 4, 8, 16, 32, 63, 125, 248, ... (OEIS A001592).
An exact formula for the 
th hexanacci number
can be given explicitly in terms of the six roots 
of
 |
(2)
|
as
 |
(3)
|
The ratio of adjacent terms tends to the positive root of 
, namely 1.98358284342...
(OEIS A118427), sometimes called the hexanacci
constant.
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hexanacci number