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 A323562 Number of rooted self-avoiding king's walks on an infinite chessboard trapped after n moves. 5
 8, 200, 2446, 21946, 169782, 1205428, 8119338, 52862872, 336465352, 2108185746 (list; graph; refs; listen; history; text; internal format)
 OFFSET 8,1 COMMENTS The first step is either (0,0)->(1,0) or (0,0)->(1,1). Rotated paths are not counted separately. The average number of moves of a self-avoiding random walk of a king on an infinite chessboard to self-trapping is 209.71. The corresponding number of moves for paths with forbidden crossing (A323141) is 69.865. a(n)=0 for n<8. LINKS Hugo Pfoertner, Probability density for the number of moves to self-trapping, (2019). EXAMPLE a(8) = 8, because the following 8 walks of 8 moves of a king starting at S with a first move (0,0)->(1,0) visit all neighbors of the trapping location T. The starting point itself is also blocked. There are no such shortest walks with first move (0,0)->(1,1). .   o <-- o <-- o   o     o <-- o   o --> o --> o   o <-- o <-- o   |           ^   ^ \ /       ^   ^           |   |           ^   v           |   | / \       |   |           v   v           |   o --> T     o   o     T     o   o     T     o   o     T     o               ^               ^     \    \    |   |   /       ^               |               |       \    \  v   v /         |   S --> o --> o   S --> o --> o   S --> o     o   o     S --> o .   S --> o --> o   S --> o --> o   S --> o     o   o     S --> o               |               |       /    /  ^   ^ \         |               v               v     /    /    |   |   \       v   o --> T     o   o     T     o   o     T     o   o     T     o   ^           |   | \ /       |   |           ^   ^           |   |           v   v / \       v   v           |   |           v   o <-- o <-- o   o     o <-- o   o --> o --> o   o <-- o <-- o - Hugo Pfoertner, Jul 23 2020 CROSSREFS Cf. A077482, A322831, A323141, A323560, A323561. Sequence in context: A020329 A232518 A229265 * A034861 A221121 A264124 Adjacent sequences:  A323559 A323560 A323561 * A323563 A323564 A323565 KEYWORD nonn,walk,more AUTHOR Hugo Pfoertner, Jan 17 2019 STATUS approved

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Last modified December 7 18:19 EST 2021. Contains 349585 sequences. (Running on oeis4.)