A323560 Number of self-avoiding knight's paths trapped after n moves on an infinite chessboard with first move specified.

1728, 10368, 332660, 1952452

Offset: 15

Author

Hugo Pfoertner, Jan 18 2019

Keywords

• nonn
• walk
• more
• hard

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.

Examples

			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.
		

Links

• Hugo Pfoertner, Illustrations of the 1728 trapped paths of length 15, (2019).
• Hugo Pfoertner, Probability density for the number of moves to self-trapping, (2019).

Crossrefs

Cf. A077482, A323141, A323559, A323562.