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A290187
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Minimum number of moves to rearrange a Tower of Hanoi puzzle with 3 colors. There are 3 rods with n discs in descending sizes. On the first rod there are n red discs, on the 2nd n blue discs and on the 3rd n white ones.
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1
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5, 23, 68, 168, 377, 801, 1657, 3377, 6825, 13729, 27545, 55185
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OFFSET
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1,1
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COMMENTS
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Like the known Tower of Hanoi you have 3 rods with n discs in descending sizes. But here on the first rod there are n red discs, on the 2nd n blue discs and on the 3rd n white ones.
The task is to rearrange the discs so that red ones go to rod 2, the blue ones to rod 3 and the white ones to rod 1. Sequence lists the number of minimum moves needed to rearrange the discs.
I have written a program to find the minimum moves, it might be improved for higher values.
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LINKS
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EXAMPLE
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For n=1 the moves are 23-12-32-31-23 (meaning to moves a disc from rod 2 to 3, then 1 to 2, ...
For n=2 the moves are 31-21-23-13-13-13-12-31-31-31-32-12-12-12-31-21-21-21-23-13-13-12-31.
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CROSSREFS
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Cf. A000225, A055622 (another 3-color variant of the Towers of Hanoi).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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