Notations:

Instead of | we denote | and we call this |

the sequence | ||

the term of index |

- Define a sequence as follows: the term with index (with ) is the digit in the decimal expansion of . We have: , , , , etc.
- The general term of can be given by an explicit formula, as in . Here we have: , , , , , .
- The general term of
can be given by a recurrence formula, as in
. In
this case, the first term of the sequence has to be given.
Take . Then , , .

- The general term of
can be given by a recurrence formula on two terms (or more). The most
famous example is Fibonacci's sequence, denoted
:

Then , , , , , , .

Noah Dana-Picard 2007-12-28