The heptanacci 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, 64, 127, 253, ... (OEIS
A066178).
For a nonnegative integer 
, an exact formula for the 
th heptanacci number is given in terms
of the seven roots 
of
 |
(2)
|
as
 |
(3)
|
The ratio of adjacent terms tends to the real root of 
,
namely 1.99196419660... (OEIS A118428), sometimes
called the heptanacci constant.
