OFFSET
0,3
REFERENCES
E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 76.
LINKS
Georg Fischer, Table of n, a(n) for n = 0..1274 (First 50 rows)
Uri Blass and Aviezri S. Fraenkel, The Sprague-Grundy function for Wythoff's game, Theoretical Computer Science 75.3 (1990): 311-333. See Table 2.
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.
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
Triangle begins as:
0;
1, 2;
2, 0, 1;
3, 4, 5, 6;
4, 5, 3, 2, 7;
5, 3, 4, 0, 6, 8;
6, 7, 8, 1, 9, 10, 3;
7, 8, 6, 9, 0, 1, 4, 5;
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}]; (* so far copied from A004481 *)
Flatten[Table[t[n, m], {n, 12}, {m, 1, n}]] (* Georg Fischer, Feb 22 2020 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Aug 07 2018
EXTENSIONS
More terms from Georg Fischer, Feb 22 2020
STATUS
approved