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%I #15 Apr 13 2019 22:18:26
%S 0,1,1,2,2,2,3,0,3,3,4,4,4,0,4,5,5,5,5,5,5,6,3,0,6,6,6,6,7,7,1,7,0,7,
%T 7,7,8,8,8,8,1,1,1,4,8,9,6,9,2,2,2,2,8,9,9,10,10,10,1,3,9,3,9,3,10,10,
%U 11,11,11,4,10,4,4,10,10,11,11,11,12,9
%N Array read by antidiagonals: Sprague-Grundy values for the game NimHof with 5 rules [1,0], [1,1], [2,3], [1,2], [0,1].
%C 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 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 Rémy Sigrist, <a href="/A307298/a307298.png">Colored representation of T(x,y) for x = 0..1023 and y = 0..1023</a> (where the hue is function of T(x,y) and black pixels correspond to zeros)
%H Rémy Sigrist, <a href="/A307298/a307298.gp.txt">PARI program for A307298</a>
%H N. J. A. Sloane, <a href="/A307298/a307298.txt">Maple program for NimHof sequences</a>
%e The initial antidiagonals are:
%e [0]
%e [1, 1]
%e [2, 2, 2]
%e [3, 0, 3, 3]
%e [4, 4, 4, 0, 4]
%e [5, 5, 5, 5, 5, 5]
%e [6, 3, 0, 6, 6, 6, 6]
%e [7, 7, 1, 7, 0, 7, 7, 7]
%e [8, 8, 8, 8, 1, 1, 1, 4, 8]
%e [9, 6, 9, 2, 2, 2, 2, 8, 9, 9]
%e [10, 10, 10, 1, 3, 9, 3, 9, 3, 10, 10]
%e [11, 11, 11, 4, 10, 4, 4, 10, 10, 11, 11, 11]
%e [12, 9, 6, 12, 11, 11, 5, 11, 11, 12, 12, 8, 12]
%e ...
%e The triangle begins:
%e [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
%e [1, 2, 3, 0, 5, 6, 7, 4, 9, 10, 11, 8]
%e [2, 0, 4, 5, 6, 7, 1, 8, 3, 11, 12]
%e [3, 4, 5, 6, 0, 1, 2, 9, 10, 12]
%e [4, 5, 0, 7, 1, 2, 3, 10, 11]
%e [5, 3, 1, 8, 2, 9, 4, 11]
%e [6, 7, 8, 2, 3, 4, 5]
%e [7, 8, 9, 1, 10, 11]
%e [8, 6, 10, 4, 11]
%e [9, 10, 11, 12]
%e [10, 11, 6]
%e [11, 9]
%e [12]
%e ...
%o (PARI) See Links section.
%Y Cf. A003987, A307296, A307297.
%K nonn,tabf
%O 0,4
%A _N. J. A. Sloane_, Apr 12 2019
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