Integer sequence

An integer sequence may be specified explicitly by giving a formula for its nth term, or implicitly by giving a relationship between its terms.

The sequence 0, 3, 8, 15, ... is formed according to the formula n2 − 1 for the nth term: an explicit definition.

An integer sequence is computable if there exists an algorithm that, given n, calculates an, for all n > 0.

The set of computable integer sequences is countable.

Although some integer sequences have definitions, there is no systematic way to define what it means for an integer sequence to be definable in the universe or in any absolute (model independent) sense.