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Partition and Fibonacci Numbers

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Partitions and the Fibonacci Numbers: A surprise!

There are eight ways to partition the number four: 4 = 3+1 = 1+3 = 2+2 = 1+1+2 = 1+2+1 = 2+1+1 = 1+1+1+1. Replace the plus signs with multiplication signs and add the products:

4 + 3x1 + 1x3 + 2x2 + 1x1x2 + 1x2x1 + 2x1x1 + 1x1x1x1 = 21.

This sum is a Fibonacci number and this is NOT a coincidence!

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