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 A323562 Number of rooted self-avoiding king's walks on an infinite chessboard trapped after n moves. 7
 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 Table of n, a(n) for n=8..17. 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 September 16 17:53 EDT 2024. Contains 375976 sequences. (Running on oeis4.)