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# Integer sequences

Formally, an integer sequence is a function (possibly partial[1]) from nonnegative integers ${\displaystyle \scriptstyle \mathbb {N} _{0}\,=\,\{0,1,2,3,...\}\,}$ to integers:
${\displaystyle f:\mathbb {N} _{0}\rightarrow \mathbb {Z} \,}$
Ideally, it should have been defined for all nonnegative integers or at least for all natural numbers ${\displaystyle \scriptstyle \mathbb {N} \,=\,\{1,2,3,...\}\,}$, but in some cases the definition is only partial[1], for example, if the offset is greater than 1, or when the sequence is finite.