A055662 - OEIS

A055662

Successive positions in Tower of Hanoi (with three pegs {0,1,2}) where 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.

0, 1, 21, 22, 122, 120, 110, 111, 2111, 2112, 2102, 2100, 2200, 2201, 2221, 2222, 12222, 12220, 12210, 12211, 12011, 12012, 12002, 12000, 11000, 11001, 11021, 11022, 11122, 11120, 11110, 11111, 211111, 211112, 211102, 211100, 211200

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

Optimal for moving an even number of disks from peg 0 to peg 2 or an odd number from peg 0 to peg 1.

LINKS

Table of n, a(n) for n=0..36.

Index entries for sequences related to Towers of Hanoi

FORMULA

a(n) = Sum_{j=0..floor(log_2(n))} 10^j * (floor((n/2^j + 1)/2)*(-1)^j mod 3).

MATHEMATICA

a[n_]:=Sum[10^j*(Mod[(-1)^j*Floor[(n/2^j + 1)/2], 3]), {j, 0, Floor[Log2[n]]}]; Array[a, 70, 0] (* Stefano Spezia, Oct 27 2018 *)