Integer sequences

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Definition

Formally, an integer sequence is a function (possibly partial) from nonnegative integers ${\mathbb{\mathbb{N}}}_0=\{0,1,2,3,...\}$ to integers:

$f:{\mathbb{\mathbb{N}}}_0\to \mathbb{\mathbb{Z}}$

Ideally, it should have been defined for all nonnegative integers or at least for all natural numbers $\mathbb{\mathbb{N}}=\{1,2,3,...\}$, but in some cases the definition is only partial, for example, if the offset is greater than 1, or when the sequence is finite.