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A307297 Array read by antidiagonals: Sprague-Grundy values for the game NimHof with 4 rules [1,0], [2,1], [3,3], [0,1].

%I A307297 #28 Jun 02 2025 13:22:11
%S A307297 0,1,1,2,0,2,3,3,3,3,4,2,0,2,4,5,5,1,1,5,5,6,4,6,4,6,4,6,7,7,7,7,0,7,
%T A307297 7,7,8,6,4,6,3,6,4,6,8,9,9,5,5,1,0,5,5,9,9,10,8,10,0,8,3,1,8,10,8,10,
%U A307297 11,11,11,11,2,9,0,2,7,11,11,11,12,10,8
%N A307297 Array read by antidiagonals: Sprague-Grundy values for the game NimHof with 4 rules [1,0], [2,1], [3,3], [0,1].
%C A307297 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 A307297 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 A307297 Rémy Sigrist, <a href="/A307297/a307297.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 A307297 Rémy Sigrist, <a href="/A307297/a307297.gp.txt">PARI program for A307297</a>
%H A307297 N. J. A. Sloane, <a href="/A307297/a307297_1.txt">Maple program for NimHof sequences</a>
%e A307297 The initial antidiagonals are:
%e A307297   [0]
%e A307297   [1, 1]
%e A307297   [2, 0, 2]
%e A307297   [3, 3, 3, 3]
%e A307297   [4, 2, 0, 2, 4]
%e A307297   [5, 5, 1, 1, 5, 5]
%e A307297   [6, 4, 6, 4, 6, 4, 6]
%e A307297   [7, 7, 7, 7, 0, 7, 7, 7]
%e A307297   [8, 6, 4, 6, 3, 6, 4, 6, 8]
%e A307297   [9, 9, 5, 5, 1, 0, 5, 5, 9, 9]
%e A307297   [10, 8, 10, 0, 8, 3, 1, 8, 10, 8, 10]
%e A307297   [11, 11, 11, 11, 2, 9, 0, 2, 7, 11, 11, 11]
%e A307297   [12, 10, 8, 10, 7, 8, 2, 9, 11, 10, 8, 10, 12]
%e A307297   ...
%e A307297 The triangle begins:
%e A307297   [1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10]
%e A307297   [2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8]
%e A307297   [3, 2, 1, 4, 0, 6, 5, 8, 7, 10]
%e A307297   [4, 5, 6, 7, 3, 0, 1, 2, 11]
%e A307297   [5, 4, 7, 6, 1, 3, 0, 9]
%e A307297   [6, 7, 4, 5, 8, 9, 2]
%e A307297   [7, 6, 5, 0, 2, 8]
%e A307297   [8, 9, 10, 11, 7]
%e A307297   [9, 8, 11, 10]
%e A307297   [10, 11, 8]
%e A307297   [11, 10]
%e A307297   [12]
%e A307297   ...
%o A307297 (PARI) \\ See Links section.
%Y A307297 Cf. A003987, A307296, etc.
%K A307297 nonn,tabf
%O A307297 0,4
%A A307297 _N. J. A. Sloane_, Apr 12 2019