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A323560
Number of self-avoiding knight's paths trapped after n moves on an infinite chessboard with first move specified.
7
1728, 10368, 332660, 1952452
OFFSET
15,1
COMMENTS
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.
a(n)=0 for n<15.
EXAMPLE
There are two (of a(15)=1728) paths of 15 moves of minimum extension 5 X 5:
(N) b1 d2 e4 c5 a4 b2 d1 e3 d5 b4 a2 c1 e2 d4 b5 c3, and
(N) a4 c5 e4 d2 b1 a3 b5 d4 e2 c1 a2 b4 d5 e3 d1 c3.
CROSSREFS
KEYWORD
nonn,walk,more,hard
AUTHOR
Hugo Pfoertner, Jan 18 2019
STATUS
approved