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).
For a nonnegative integer 
, an exact formula for the 
th hexanacci number is given 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.
