The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)



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.


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).


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.


Cf. A077482, A323141, A323559, A323562.

Sequence in context: A179694 A202200 A251188 * A223236 A017403 A017523

Adjacent sequences:  A323557 A323558 A323559 * A323561 A323562 A323563




Hugo Pfoertner, Jan 18 2019



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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