The number f(n) of steps required to solve the "chinese rings
puzzle" with n ring satisfies f(1) = 1 and
f(n+1) = 2f(n) if n is odd,
2f(n) + 1 if n is even.
Prove that f(n+2) = f(n+1) + 2f(n) + 1. Hence or otherwise
find a formula for f(n) in term of n.
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