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A307300 Array read by antidiagonals: Sprague-Grundy values for the game NimHof with rules [1,0], [2,2], [0,1].

%I A307300 #13 Apr 13 2019 22:18:41
%S A307300 0,1,1,2,0,2,3,3,3,3,4,2,1,2,4,5,5,0,0,5,5,6,4,6,1,6,4,6,7,7,7,7,7,7,
%T A307300 7,7,8,6,5,6,2,6,5,6,8,9,9,4,4,3,3,4,4,9,9,10,8,10,5,0,2,0,5,10,8,10,
%U A307300 11,11,11,11,1,1,1,1,11,11,11,11,12,10
%N A307300 Array read by antidiagonals: Sprague-Grundy values for the game NimHof with rules [1,0], [2,2], [0,1].
%C A307300 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 A307300 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 A307300 Rémy Sigrist, <a href="/A307300/a307300.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 A307300 Rémy Sigrist, <a href="/A307300/a307300.gp.txt">PARI program for A307300</a>
%H A307300 N. J. A. Sloane, <a href="/A307296/a307296.txt">Maple program for NimHof sequences</a>
%e A307300 The initial antidiagonals are:
%e A307300 [0]
%e A307300 [1, 1]
%e A307300 [2, 0, 2]
%e A307300 [3, 3, 3, 3]
%e A307300 [4, 2, 1, 2, 4]
%e A307300 [5, 5, 0, 0, 5, 5]
%e A307300 [6, 4, 6, 1, 6, 4, 6]
%e A307300 [7, 7, 7, 7, 7, 7, 7, 7]
%e A307300 [8, 6, 5, 6, 2, 6, 5, 6, 8]
%e A307300 [9, 9, 4, 4, 3, 3, 4, 4, 9, 9]
%e A307300 [10, 8, 10, 5, 0, 2, 0, 5, 10, 8, 10]
%e A307300 [11, 11, 11, 11, 1, 1, 1, 1, 11, 11, 11, 11]
%e A307300 [12, 10, 9, 10, 12, 0, 3, 0, 12, 10, 9, 10, 12]
%e A307300 ...
%e A307300 The triangle begins:
%e A307300 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
%e A307300 [1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10]
%e A307300 [2, 3, 1, 0, 6, 7, 5, 4, 10, 11, 9]
%e A307300 [3, 2, 0, 1, 7, 6, 4, 5, 11, 10]
%e A307300 [4, 5, 6, 7, 2, 3, 0, 1, 12]
%e A307300 [5, 4, 7, 6, 3, 2, 1, 0]
%e A307300 [6, 7, 5, 4, 0, 1, 3]
%e A307300 [7, 6, 4, 5, 1, 0]
%e A307300 [8, 9, 10, 11, 12]
%e A307300 [9, 8, 11, 10]
%e A307300 [10, 11, 9]
%e A307300 [11, 10]
%e A307300 [12]
%e A307300 ...
%o A307300 (PARI) See Links section.
%Y A307300 Cf. A003987, A307296, A307297.
%K A307300 nonn,tabf
%O A307300 0,4
%A A307300 _N. J. A. Sloane_, Apr 13 2019