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A004481
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Table of Sprague-Grundy values for Wythoff's game (Wyt Queens) read by antidiagonals.
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13
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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, 2, 2, 4, 7, 7, 8, 8, 8, 0, 7, 0, 8, 8, 8, 9, 6, 6, 1, 6, 6, 1, 6, 6, 9, 10, 10, 7, 9, 9, 8, 9, 9, 7, 10, 10, 11, 11, 11, 10, 0, 10, 10, 0, 10, 11, 11, 11, 12, 9, 9, 12, 1, 1, 3, 1, 1, 12, 9, 9, 12
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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T(a,b) = T(b,a).
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REFERENCES
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E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 76.
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?
R. K. Guy, The unity of combinatorics, Proc. 25th Iranian Math. Conf, Tehran, (1994), Math. Appl 329 129-159, Kluwer Dordrecht 1995, Math. Rev. 96k:05001.
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LINKS
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EXAMPLE
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Table begins
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
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, 2, 0, 1, 9, 10, 12, ...
4, 5, 3, 2, 7, 6, 9, 0, 1, ...
5, 3, 4, 0, 6, 8, 10, 1, ...
6, 7, 8, 1, 9, 10, 3, ...
7, 8, 6, 9, 0, 1, ...
8, 6, 7, 10, 1, ...
9, 10, 11, 12, ...
10, 11, 9, ...
11, 9, ...
12, ...
...
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MATHEMATICA
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mex[list_] := mex[list] = Min[Complement[Range[0, Length[list]], list]];
move[Wnim, {a_, b_}] := move[Wnim, {a, b}] =
Union[Table[{i, b}, {i, 0, a - 1}], Table[{a, i}, {i, 0, b - 1}],
Table[{a - i, b - i}, {i, 1, Min[a, b]}]];
SpragueGrundy[game_, list_] := SpragueGrundy[game, list] =
mex[SpragueGrundy[game, #] & /@ move[game, list]];
t[n_, m_] := SpragueGrundy[Wnim, {n - 1, m - 1}];
Flatten@Table[t[n - m + 1, m], {n, 11}, {m, n}] (* Birkas Gyorgy, Apr 19 2011 *)
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PROG
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(PARI) See Links section.
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CROSSREFS
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See A317205 for triangle of values on or below main diagonal.
Similar to but different from A004489.
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KEYWORD
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AUTHOR
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STATUS
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approved
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