A323699 Number of uncrossed knight's walks as specified in A323700, counting isomorphisms only once.

1, 8, 56, 404, 2563, 16516, 102280, 639532, 3899662

Offset

4,2

Comments

First differs at a(7)=404 from A323700(7)=406, because there are two walks of length 7 trapped at both ends. If seen as unrooted walks, their path shapes become identical after path reversal and reflection.

Links

Table of n, a(n) for n=4..12.

Hugo Pfoertner, Illustrations of uncrossed knight's walks trapped after n moves, (2019).

Hugo Pfoertner, Probability density for the number of moves to self-trapping, (2019).

Example

In algebraic chess notation, the two walks double counted in A323700(7) are
  N c4 d2 e4 c5 a4 b2 d1 c3 and N d4 c2 e3 d5 b4 a2 c1 b3.

Crossrefs

Cf. A003192, A323131, A323559, A323560, A323700.

Sequence in context: A252701 A033134 A126985 * A323700 A182430 A027081

Adjacent sequences: A323696 A323697 A323698 * A323700 A323701 A323702

Keyword

nonn,walk,hard,more

Author

Hugo Pfoertner, Jan 24 2019

Status

approved