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

Author

Hugo Pfoertner, Jan 24 2019

Keywords

• nonn
• walk
• more
• hard

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.

Examples

			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.