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A323560 Number of self-avoiding knight's paths trapped after n moves on an infinite chessboard with first move specified. 6
1728, 10368, 332660, 1952452 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=15..18.

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).

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

Cf. A077482, A323141, A323559, A323562.

Sequence in context: A179694 A202200 A251188 * A223236 A017403 A017523

Adjacent sequences:  A323557 A323558 A323559 * A323561 A323562 A323563

KEYWORD

nonn,walk,more,hard

AUTHOR

Hugo Pfoertner, Jan 18 2019

STATUS

approved

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Last modified December 4 04:49 EST 2021. Contains 349469 sequences. (Running on oeis4.)