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A307296
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Array read by antidiagonals: Sprague-Grundy values for the game NimHof with 4 rules [1,0], [3,2], [1,1], [0,1],
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7
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0, 1, 1, 2, 2, 2, 3, 0, 0, 3, 4, 4, 1, 4, 4, 5, 5, 5, 5, 5, 5, 6, 3, 3, 6, 3, 3, 6, 7, 7, 4, 7, 7, 4, 7, 7, 8, 8, 8, 1, 8, 0, 8, 8, 8, 9, 6, 6, 0, 2, 2, 1, 6, 6, 9, 10, 10, 7, 2, 9, 7, 9, 2, 7, 10, 10, 11, 11, 11, 9, 10, 10, 10, 0, 9, 11, 11, 11, 12, 9, 9, 12, 0, 11, 3, 11, 1, 12, 9, 9, 12
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listen;
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OFFSET
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0,4
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COMMENTS
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The game NimHof with a list of rules R means that for each rule [a,b] you can move from cell [x,y] to any cell [x-i*a,y-i*b] as long as neither coordinate is negative. See the Friedman et al. article for further details.
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REFERENCES
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Eric Friedman, Scott M. Garrabrant, Ilona K. Phipps-Morgan, A. S. Landsberg and Urban Larsson, Geometric analysis of a generalized Wythoff game, in Games of no Chance 5, MSRI publ. Cambridge University Press, date?
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LINKS
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EXAMPLE
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The initial antidiagonals are:
[0],
[1, 1],
[2, 2, 2],
[3, 0, 0, 3],
[4, 4, 1, 4, 4],
[5, 5, 5, 5, 5, 5],
[6, 3, 3, 6, 3, 3, 6],
[7, 7, 4, 7, 7, 4, 7, 7],
[8, 8, 8, 1, 8, 0, 8, 8, 8],
[9, 6, 6, 0, 2, 2, 1, 6, 6, 9],
[10, 10, 7, 2, 9, 7, 9, 2, 7, 10, 10],
[11, 11, 11, 9, 10, 10, 10, 0, 9, 11, 11, 11],
[12, 9, 9, 12, 0, 11, 3, 11, 1, 12, 9, 9, 12],
The triangle begins:
[1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9]
[2, 0, 1, 5, 3, 4, 8, 6, 7, 11, 9]
[3, 4, 5, 6, 7, 0, 1, 2, 9, 12]
[4, 5, 3, 7, 8, 2, 9, 0, 1]
[5, 3, 4, 1, 2, 7, 10, 11]
[6, 7, 8, 0, 9, 10, 3]
[7, 8, 6, 2, 10, 11]
[8, 6, 7, 9, 0]
[9, 10, 11, 12]
[10, 11, 9]
[11, 9]
[12]
...
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PROG
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(PARI) See Links section.
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CROSSREFS
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List of NimHof sequences:
A-number Rules R
A307298 [1,0], [1,1], [1,2], [2,3], [0,1]
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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