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Search: id:A096367
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| A096367 |
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Number of winning paths of length n+1 across an n X n Hex board. |
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+0
2
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| 2, 14, 58, 194, 578, 1602, 4226, 10754, 26626, 64514, 153602, 360450, 835586, 1916930, 4358146, 9830402, 22020098, 49020930, 108527618, 239075330, 524288002, 1145044994
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OFFSET
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3,1
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COMMENT
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If m>n-2, H(m,n) = (2*m+1-n)*2^(n-2) is the number of winning paths of length n across an m X n Hex board (cf. A001792). If m>n-1, H'(m,n) = (n-2)*(H(m-3,n-2) + H(m+1,n-2)) - 2^(n-1) + 2 is the number of winning paths of length n+1 across an m X n Hex board.
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REFERENCES
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D. Bevan, Winning Positions and Optimal Play in the Game of Hex, forthcoming.
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FORMULA
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a(n) = (n-2)*(n+1)*2^(n-3)-2^(n-1)+2
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EXAMPLE
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a(4)=14.
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CROSSREFS
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Cf. A001792.
Sequence in context: A137482 A115027 A114146 this_sequence A058738 A095376 A153332
Adjacent sequences: A096364 A096365 A096366 this_sequence A096368 A096369 A096370
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KEYWORD
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nonn
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AUTHOR
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David Bevan (dbevan(AT)emtex.com), Jul 02 2004
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