Polynomial recurrence
Encyclopedia
In mathematics, a sequence 
, 
obeys a polynomial recurrence of length 
if there is a nonzero polynomial 
such that
This is at variance with the usual use of the term recurrence
which would be more like
The Somos sequence
s form examples of integer sequence
s generated by a recurrence of this type.
, obeys a polynomial recurrence of length if there is a nonzero polynomial such that
This is at variance with the usual use of the term recurrence
Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms....
which would be more like
-
Of course this could be transformed into one of the previous form but the converse is not true.
The Somos sequence
Somos sequence
In mathematics, a Somos sequence is a sequence of numbers defined by a bilinear recurrence relation, discovered by mathematician Michael Somos. It is not obvious from the form of their defining recurrence that every number in a Somos sequence is an integer, but nevertheless many Somos sequences...
s form examples of integer sequence
Integer sequence
In mathematics, an integer sequence is a sequence of integers.An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms...
s generated by a recurrence of this type.