Definition:Fibonacci-Like Sequence

From ProofWiki
Jump to navigation Jump to search


Let $A = \tuple {a_0, a_1, \ldots, a_{n - 1} }$ be an ordered tuple of numbers.

The Fibonacci-like sequence formed from $A$ is defined as:

$\map {F_A} k = \begin {cases} \qquad \qquad a_k & : 0 \le k < n \\ & \\ \ds \sum_{k - n \mathop \le j \mathop < k} a_j & : k \ge n \end {cases}$

That is, apart from the first $n$ terms, every term is the sum of the previous $n$ terms.

The main term can also be expressed as:

$\map {F_A} k = 2 \map {F_A} {k - 1} - \map {F_A} {k - n}$

Also see