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A307296 Array read by antidiagonals: Sprague-Grundy values for the game NimHof with 4 rules [1,0], [3,2], [1,1], [0,1].

%I A307296 #29 Jun 02 2025 13:27:06
%S A307296 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,
%T A307296 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,
%U A307296 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
%N A307296 Array read by antidiagonals:  Sprague-Grundy values for the game NimHof with 4 rules [1,0], [3,2], [1,1], [0,1].
%C A307296 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.
%D A307296 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?
%H A307296 Rémy Sigrist, <a href="/A307296/a307296.png">Colored representation of T(x,y) for x = 0..999 and y = 0..999</a> (where the hue is function of T(x,y) and black pixels correspond to zeros)
%H A307296 Rémy Sigrist, <a href="/A307296/a307296.gp.txt">PARI program for A307296</a>
%H A307296 N. J. A. Sloane, <a href="/A307296/a307296.txt">Maple program for NimHof sequences</a>
%e A307296 The initial antidiagonals are:
%e A307296   [0],
%e A307296   [1, 1],
%e A307296   [2, 2, 2],
%e A307296   [3, 0, 0, 3],
%e A307296   [4, 4, 1, 4, 4],
%e A307296   [5, 5, 5, 5, 5, 5],
%e A307296   [6, 3, 3, 6, 3, 3, 6],
%e A307296   [7, 7, 4, 7, 7, 4, 7, 7],
%e A307296   [8, 8, 8, 1, 8, 0, 8, 8, 8],
%e A307296   [9, 6, 6, 0, 2, 2, 1, 6, 6, 9],
%e A307296   [10, 10, 7, 2, 9, 7, 9, 2, 7, 10, 10],
%e A307296   [11, 11, 11, 9, 10, 10, 10, 0, 9, 11, 11, 11],
%e A307296   [12, 9, 9, 12, 0, 11, 3, 11, 1, 12, 9, 9, 12],
%e A307296 The triangle begins:
%e A307296   [1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9]
%e A307296   [2, 0, 1, 5, 3, 4, 8, 6, 7, 11, 9]
%e A307296   [3, 4, 5, 6, 7, 0, 1, 2, 9, 12]
%e A307296   [4, 5, 3, 7, 8, 2, 9, 0, 1]
%e A307296   [5, 3, 4, 1, 2, 7, 10, 11]
%e A307296   [6, 7, 8, 0, 9, 10, 3]
%e A307296   [7, 8, 6, 2, 10, 11]
%e A307296   [8, 6, 7, 9, 0]
%e A307296   [9, 10, 11, 12]
%e A307296   [10, 11, 9]
%e A307296   [11, 9]
%e A307296   [12]
%e A307296   ...
%o A307296 (PARI) \\ See Links section.
%Y A307296 List of NimHof sequences:
%Y A307296 A-number    Rules R
%Y A307296 A003987  [1,0], [0,1]
%Y A307296 A004481  [1,0], [1,1], [0,1]
%Y A307296 A003987  [1,0], [2,1], [0,1]
%Y A307296 A307300  [1,0], [2,2], [0,1]
%Y A307296 A307301  [1,0], [3,1], [0,1]
%Y A307296 A003987  [1,0], [3,2], [0,1]
%Y A307296 A307302  [1,0], [3,3], [0,1]
%Y A307296 A307299  [1,0], [1,1], [1,2], [0,1]
%Y A307296 A307296  [1,0], [1,1], [3,2], [0,1]
%Y A307296 A307297  [1,0], [2,1], [3,3], [0,1]
%Y A307296 A307298  [1,0], [1,1], [1,2], [2,3], [0,1]
%K A307296 nonn,tabf
%O A307296 0,4
%A A307296 _N. J. A. Sloane_, Apr 12 2019