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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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9
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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; internal format)
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OFFSET
| 0,4
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COMMENTS
| T(a,b) = T(b,a).
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REFERENCES
| E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 76.
A. Dress, A. Flammenkamp and N. Pink, Additive periodicity of the Sprague-Grundy function of certain Nim games, Adv. Appl. Math., 22, p. 249-270 (1999).
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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EXAMPLE
| Table begins
0 1 2 3 4 5 ...
1 2 0 4 5 3 ...
2 0 1 5 3 4 ...
3 4 5 6 2 0 ...
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MATHEMATICA
| 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}] (* Gyorgy Birkas Apr 19, 2011 *)
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CROSSREFS
| A004482-A004487 are rows 1 to 6. Cf. A047708.
Similar to but different from A004489.
T(a, b)=0 iff A018219(a, b)=0 iff A002251(a)=b.
Sequence in context: A049300 A084957 A035307 * A004489 A112599 A106795
Adjacent sequences: A004478 A004479 A004480 * A004482 A004483 A004484
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KEYWORD
| nonn,tabl,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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