%I #17 Mar 25 2021 19:02:54

%S 1,2,1,3,1,2,4,5,1,2,1,3,1,5,4,3,1,2,1,3,1,2,4,5,1,2,4,3,1,5,4,5,1,2,

%T 1,3,1,2,4,5,1,2,1,3,1,5,4,3,1,2,1,3,1,5,4,5,1,2,4,3,1,5,4,3,1,2,1,3,

%U 1,2,4,5,1,2,1,3,1,5,4,3,1,2,1,3,1,2,4

%N a(n) = one of five triples of directions in n-th triple of moves in the optimal solution of the Tower of Hanoi; it is a squarefree sequence over a five-letter alphabet.

%C To construct a(n), consider the six consecutive terms A101608(6*n-5) through A101608(6*n) as a single string (e.g., for n=1 we have 121323, for n=2 we have 123132). Only five different strings occur, corresponding to the five letter alphabet used here. Apply the mapping 121323 -> 1, 123132 -> 2, 213123 -> 3, 123123 -> 4, 213132 -> 5. - _Sean A. Irvine_, Mar 24 2021

%D Andreas M. Hinz, The Tower of Hanoi, in Algebras and combinatorics (Hong Kong, 1997), 277-289, Springer, Singapore, 1999.

%H Andreas M. Hinz, <a href="http://dx.doi.org/10.5169/seals-87878">Squarefree Tower of Hanoi sequences</a>, Enseign. Math. (2) 42(1996), 257-264.

%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>

%Y Cf. A101608.

%K nonn

%O 1,2

%A _Andreas M. Hinz_, Dec 11 1999

%E More terms from _Sean A. Irvine_, Mar 24 2021