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.
