A323141 Number of self-trapped uncrossed king's paths on an infinite board after n steps, reduced for symmetry.

0, 0, 0, 0, 2, 19, 150, 1043, 6843, 43192, 266529, 1619983, 9746883, 58220994, 345919915

Offset: 1

Author

Hugo Pfoertner, Jan 05 2019

Keywords

• nonn
• walk
• hard
• more

Comments

The average number of moves of a self-avoiding uncrossed random walk of a king on an infinite chessboard to self-trapping is 69.865+-0.008. - Hugo Pfoertner, Oct 22 2024

Examples

			a(5) = 2: There are 2 walks where the king is blocked after 5 steps, because for the diagonal moves it would have to cross its previous path.
.
  o       2       o       o       3        o
        /   \                   /   \
      /       \               /        \
    /           \           /            \
  3       5       1       4 - - - 5        2
  |     /       /                        /
  |   /       /                        /
  | /       /                        /
  4       S       o       S - - -  1       o
		

Links

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

Crossrefs

Cf. A003192, A077482, A272773, A323140, A323562.