Heptanacci Number
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.
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heptanacci number