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A323141
Number of self-trapped uncrossed king's paths on an infinite board after n steps, reduced for symmetry.
6
0, 0, 0, 0, 2, 19, 150, 1043, 6843, 43192, 266529, 1619983, 9746883, 58220994, 345919915
OFFSET
1,5
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
EXAMPLE
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
CROSSREFS
KEYWORD
nonn,walk,hard,more
AUTHOR
Hugo Pfoertner, Jan 05 2019
STATUS
approved