Who invented the Fibonacci sequence?

Leonardo Fibonacci wrote about recreational mathematics, some of which involved number series such as the Fibonacci series that he is credited with discovering.

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It is said that he was moDELLing rabbit population when he came up with the sequence that now bears his name. The rules are simple:

1. Rabbits that are one year old are juveniles and do not breed.

2. Each pair of rabbits aged two or more produce a pair of rabbit each year (forever!).

3. No rabbits ever die (what?).

The whole process could apply to periods shorter than a year.

Year 1: One pair of rabbits aged 0.

Year 2: One pair of juvenile rabbits.

Year 3: One pair of mature rabbits + One pair offspring aged 0 = 2 pairs

Year 4: One pair mature + One pair offspring age 0 + One pair juvenile = 3 pairs

Year 5: Two pair mature + One pair offspring age 0 + One pair juvenile + one pair offspring age 0 (from the newly mature) = 5

and so on.

This model is a pretty poor descriptor for a rabbit population so I suspect it is not true. But makes an interesting exercise for young minds.