A323700 Number of rooted uncrossed knight's walks on an infinite chessboard trapped after n moves with first move specified.

1, 8, 56, 406, 2572, 16596, 102654, 642441, 3914084

Offset

4,2

Comments

Trapping occurs if the walk cannot be continued without reusing an already visited field or creating an intersection of the path segments formed by straight lines connecting consecutively visited fields.

The shortest self-trapped walk has 4 moves, i.e., a(n)=0 for n < 4.

Links

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

Example

a(4) = 1 because there is only one trapped walk of 4 moves, written in algebraic chess notation: (N) b1 d2 b3 a1 c2.
For longer walks see link to illustrations in A323699.

Crossrefs

Cf. A003192, A323131, A323559, A323560, A323699.

Sequence in context: A033134 A126985 A323699 * A182430 A027081 A093134

Adjacent sequences: A323697 A323698 A323699 * A323701 A323702 A323703

Keyword

nonn,walk,more,hard

Author

Hugo Pfoertner, Jan 24 2019

Status

approved