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Generalizations of Fibonacci numbers

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In mathematics, the Fibonacci numbers form a sequence defined recursively by:

A geometric construction of the Tribonacci constant (AC), with compass and marked ruler, according to the method described by Xerardo Neira.

Fibonacci sequence

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In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . The sequence commonly starts from 0 and 1, although some authors start the sequence from 1 and 1 or sometimes from 1 and 2. Starting from 0 and 1, the sequence begins0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ....

A page of Fibonacci's Liber Abaci from the Biblioteca Nazionale di Firenze showing (in box on right) 13 entries of the Fibonacci sequence: the indices from present to XII (months) as Latin ordinals and Roman numerals and the numbers (of rabbit pairs) as Hindu-Arabic numerals starting with 1, 2, 3, 5 and ending with 377.