An odd symmetry

pF(000 111010001) => (1,2,3,5,8,13,18,31,44,62,93,155)

111010001 backwards is 100010111

pF(000 100010111) => (1,2,3,5,7,10,15,25,35,60,95,155).

Definition 4.1. For a e {0,1} *, let a^R refer to the reversal of a; that is, the string a written backward.

Example: If a=00010, then a^R=01000 and if a=01010, then a=a^R.

Theorem 4.2. For each a e {0,1} *, pF(000a) = pF(000a^R).

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