Will rate LIFESAVER!! You haw the standard Tower of Hanoi situation (3 pegs and

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Will rate LIFESAVER!!

You haw the standard Tower of Hanoi situation (3 pegs and n discs of sizes 1,2.3.....n). As usual, you can move one disc at a time from one peg to another one provided you don't place a larger disc on top of a smaller one. In this variation, it costs you A-2 dollars to move a disc of size k. What is the minimum cost C{n) you can pay in order to move the entire stack on n discs to another peg? For example, it is easy to see that C(l) = 1. C(2) = 6 and C(3) = 21. Find an explicit form for C(n). (Hint: find a recurrence for C(n) and then solve the recurrence).

Explanation / Answer

I don't know why this is statistics: 1, 1+1+4, 1+1+1+1+4+4+9 is the work for those. If so we just double the necessary amount: 1*8+4*4+9*2+16 1*16+4*8+9*4+16*2+25 http://oeis.org/A047520 It's a series known with the closed form: a(n) = 2*a(n-1) + n^2

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