1, 2, 5, 13, 34, 89, ... follows the sequence F

_{n+1}= 3F

_{n}- F

_{n-1}.

1, 3, 8, 21, 55, 144, ... follows the same sequence as well.

The astonishing conclusion is that the Fibonacci sequence, obtained by simply adding together the two previous terms, is also a composition of two like sequences that differ only in their second term!