Integer sequences

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Definition

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

$f:\mathbb {N} _{0}\rightarrow \mathbb {Z} \,$

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