Enanacci numbers

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The enanacci numbers (the prefix ένα being 'one' in Greek) (1-bonacci numbers) are degenerate N-bonacci numbers. (Cf. Category:Recurrence, linear, order 01, (1)).

Abiding by the following definition of N-bonacci numbers

The N-bonacci numbers arise from a recurrence relation like that of the Fibonacci numbers, but with $\scriptstyle N$ initial terms defined as

${\begin{array}{rcl}a(n)&:=&0,\quad 0\leq n\leq N-2;\\a(N-1)&:=&1;\end{array}}$

instead of two initial terms, and where each subsequent term is the sum of the previous $\scriptstyle N$ terms

$a(n):=\sum _{i=n-N}^{n-1}a(i),\quad n\geq N.$

With $\scriptstyle N\,=\,1\,$, we thus have $\scriptstyle a(0)\,=\,1;\;a(n)\,=\,a(n-1),\,n\,\geq \,1.$ This begets the all 1's sequence.

A000012 The simplest sequence of positive numbers: the all 1's sequence.

{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...}

See also

• Medenacci numbers (0-bonacci numbers)

External links

• Greek Numbers and Numerals (Ancient and Modern)