The two recursive sequences
 |  |  |
(1)
|
 |  |  |
(2)
|
with 
, 
and 
, 
, can be solved for the individual 
and 
. They are given by
 |  |  |
(3)
|
 |  |  |
(4)
|
where
 |  |  |
(5)
|
 |  |  |
(6)
|
 |  |  |
(7)
|
A useful related identity is
 |
(8)
|
Binet's formula is a special case of the Binet form for 
corresponding to 
.
