%I #19 Jan 30 2019 05:20:16
%S 1728,10368,332660,1952452
%N Number of self-avoiding knight's paths trapped after n moves on an infinite chessboard with first move specified.
%C The average number of moves of a self-avoiding random walk of a knight on an infinite chessboard to self-trapping is 3210. The corresponding number of moves for paths with forbidden crossing (A323131) is 45.
%C a(n)=0 for n<15.
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a323560.htm">Illustrations of the 1728 trapped paths of length 15</a>, (2019).
%H Hugo Pfoertner, <a href="/A323560/a323560.pdf">Probability density for the number of moves to self-trapping</a>, (2019).
%e There are two (of a(15)=1728) paths of 15 moves of minimum extension 5 X 5:
%e (N) b1 d2 e4 c5 a4 b2 d1 e3 d5 b4 a2 c1 e2 d4 b5 c3, and
%e (N) a4 c5 e4 d2 b1 a3 b5 d4 e2 c1 a2 b4 d5 e3 d1 c3.
%Y Cf. A077482, A323141, A323559, A323562.
%K nonn,walk,more,hard
%O 15,1
%A _Hugo Pfoertner_, Jan 18 2019