No, patterns with terms that are not based upon previous terms are not recursive.
Example: i * i where i is the nth term of the pattern.
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The term recursive refers to the recurrence or repetition.
A recursive rule is one which can be applied over and over again to its own output
1) Recursive algorithms 2) Basic Principle 3) Analysis
Infinitely many. For example: Un+1 = Un + 3 or Un+1 = 2*Un - 1 or Un+1 = 3*Un - 5 or, more generally, Un+1 = k*Un + 7 - 4*k where k is any number. Each one of them will be different from the third term onwards. These are linear patterns. There are quadratic and other recursive relationships.
Without an equality sign it is no kind of an equation at all.