%I #16 Oct 22 2024 07:59:41
%S 0,0,0,0,2,19,150,1043,6843,43192,266529,1619983,9746883,58220994,
%T 345919915
%N Number of self-trapped uncrossed king's paths on an infinite board after n steps, reduced for symmetry.
%C 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
%H Hugo Pfoertner, <a href="/A323141/a323141.pdf">Probability density for the number of moves to self-trapping</a>, (2019).
%e 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.
%e .
%e o 2 o o 3 o
%e / \ / \
%e / \ / \
%e / \ / \
%e 3 5 1 4 - - - 5 2
%e | / / /
%e | / / /
%e | / / /
%e 4 S o S - - - 1 o
%Y Cf. A003192, A077482, A272773, A323140, A323562.
%K nonn,walk,hard,more
%O 1,5
%A _Hugo Pfoertner_, Jan 05 2019