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A004481 Table of Sprague-Grundy values for Wythoff's game (Wyt Queens) read by antidiagonals. 10
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)
OFFSET

0,4

COMMENTS

T(a,b) = T(b,a).

REFERENCES

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 76.

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.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..5049

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).

Gabriel Nivasch, More on the Sprague-Grundy function for Wythoff’s game, pages 377-410 in "Games of No Chance 3, MSRI Publications Volume 56, 2009. See Table 1.

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 ...

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}] (* Birkas Gyorgy, Apr 19 2011 *)

CROSSREFS

A004482-A004487 are rows 1 to 6. Cf. A047708 (main diagonal).

Similar to but different from A004489.

T(a, b)=0 iff A018219(a, b)=0 iff A002251(a)=b.

Sequence in context: A239944 A235812 A035307 * A004489 A112599 A216674

Adjacent sequences:  A004478 A004479 A004480 * A004482 A004483 A004484

KEYWORD

nonn,tabl,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 27 22:57 EDT 2017. Contains 287210 sequences.