%I #11 Jan 20 2021 03:47:32
%S 0,1,1,1,0,1,3,1,1,3,3,3,0,3,3,2,3,2,2,3,2,3,2,2,0,2,2,3,2,2,1,1,1,1,
%T 2,2,3,1,3,1,0,1,3,1,3,7,2,2,1,1,1,1,2,2,7,6,6,3,2,2,0,2,2,3,6,6,7,5,
%U 7,2,3,2,2,3,2,7,5,7,6,6,6,6,3,3,0,3,3,6,6,6,6,7,5,7,5,5,3,1,1,3,5,5,7,5,7
%N Square table by antidiagonals of minimum number of moves between two positions in the Tower of Hanoi (with three pegs: 0,1,2), where with position n written in base 3, xyz means smallest disk is on peg z, second smallest is on peg y, third smallest on peg x, etc. and leading zeros indicate largest disks are all on peg 0.
%H Henry Bottomley, <a href="/A060592/a060592.gif">Graph of positions and possible routes on a Sierpinski triangle</a>
%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%e T(4,9)=5 since 4 and 9 written in base 3 are 11 and 100, i.e. the starting position has the first and second disks on peg 1 and the others on peg 0, while the end position has the third disk on peg 1 and the others on peg 0; the five optimal moves between these positions are: move the third disk to peg 2, then the first to peg 2, the second to peg 0, the first to peg 0 and finally the third to peg 1.
%Y Cf. A001511, A007798, A055661, A055662.
%K nonn,tabl
%O 0,7
%A _Henry Bottomley_, Apr 06 2001