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A323560
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Number of self-avoiding knight's paths trapped after n moves on an infinite chessboard with first move specified.
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6
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OFFSET
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15,1
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COMMENTS
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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.
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LINKS
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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).
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EXAMPLE
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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.
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CROSSREFS
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Cf. A077482, A323141, A323559, A323562.
Sequence in context: A179694 A202200 A251188 * A223236 A017403 A017523
Adjacent sequences: A323557 A323558 A323559 * A323561 A323562 A323563
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KEYWORD
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nonn,walk,more,hard
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AUTHOR
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Hugo Pfoertner, Jan 18 2019
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STATUS
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approved
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