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Number of self-trapped uncrossed king's paths on an infinite board after n steps, reduced for symmetry.
6

%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