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A290187 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.

%I A290187 #37 Nov 23 2024 08:28:57
%S A290187 5,23,68,168,377,801,1657,3377,6825,13729,27545,55185
%N A290187 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.
%C A290187 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.
%C A290187 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.
%C A290187 I have written a program to find the minimum moves, it might be improved for higher values.
%H A290187 Cut The Knot, <a href="http://www.cut-the-knot.org/Curriculum/Combinatorics/Hanoi3c.shtml">3-Colors Tower of Hanoi</a>
%H A290187 Bodo Zinser, <a href="/A290187/a290187.txt">Tower of Hanoi with three colors</a> (explanation of the algorithm)
%H A290187 <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%e A290187 For n=1 the moves are 23-12-32-31-23 (meaning to move a disc from rod 2 to 3, then 1 to 2, ...).
%e A290187 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.
%Y A290187 Cf. A000225, A055622 (another 3-color variant of the Towers of Hanoi).
%K A290187 nonn,more
%O A290187 1,1
%A A290187 _Bodo Zinser_, Jul 23 2017