One of the numbers in the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13,…, where each number after the second is the sum of the two preceding numbers in the sequence. This sequence has many interesting properties. For instance, the sequence consisting of the ratios of one Fibonacci number to the previous one, has the limit τ, the golden ratio. See also difference equation and generating function.
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/ A site with examples of Fibonacci numbers in nature and the relationship to the Golden section.