[seqfan] Knight's tours

[Mason John]

Dear Seqfans

A few years ago, a sequence was posted containing the representations of free polyominoes (A246559).
Following that idea, this post concerns the representations of closed knight's tours.
Any tour may be represented by a series of digits, between 1 and 8, such that 1 corresponds to some direction of the knight, say north-north-east, then 2 is east-north-east and so on.

So possible sequences could be:

Sequence 1: Lexicographically minimal sequence of 64 moves of a knight forming a closed tour on an 8 by 8 chessboard.
1,1,1,2,3,5,4,5,7,1,1,1,6,3,5,4,6,1,4,7,6,1,1,1,4,7,1,6,5,5,2,5,6,8,1,3,1,8,6,5,3,5,8,1,8,3,2,5,8,6,3,8,5,4,5,3,1,1,4,2,5,6,7,6

Sequence 2: 64-digit representations of closed knight's tours in ascending order.

1112354571116354614761114716552568131865358183258638545311425676,
1112354571116354614761114716552568182416745412425685718146124556,
1112354571116354614761114716552568182416745412557181461245325676,
1112354571116354614761114716552568182416745417124588545311425676,
1112354571116354614761114716552568182416745425718143671245325676

Sequence 3: Closed knight's tours on 2n by 2n chessboards having minimal representations, for n >= 3.
112546147257618235618527453218527654,
1112354571116354614761114716552568131865358183258638545311425676,
1111234545711163546147611147116555252256711611252755525585711186313555478181325575346818146183245556

Interesting?

john