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).
An exact formula for the 
th heptanacci number can be given explicitly 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.
