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A307299 Array read by antidiagonals: Sprague-Grundy values for the game NimHof with 4 rules [1,0], [1,1], [1,2], [0,1].

%I A307299 #25 Jun 02 2025 12:53:09
%S A307299 0,1,1,2,2,2,3,0,3,3,4,4,4,0,4,5,5,5,5,5,5,6,3,0,1,1,6,6,7,7,1,2,0,7,
%T A307299 7,7,8,8,8,6,3,8,3,4,8,9,6,9,4,7,9,2,8,9,9,10,10,10,10,9,10,10,9,10,
%U A307299 10,10,11,11,11,11,2,3,4,1,6,6,11,11,12,9
%N A307299 Array read by antidiagonals: Sprague-Grundy values for the game NimHof with 4 rules [1,0], [1,1], [1,2], [0,1].
%C A307299 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 A307299 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 A307299 Rémy Sigrist, <a href="/A307299/a307299.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 A307299 Rémy Sigrist, <a href="/A307299/a307299.gp.txt">PARI program for A307299</a>
%H A307299 N. J. A. Sloane, <a href="/A307299/a307299.txt">Maple program for NimHof sequences</a>
%e A307299 The initial antidiagonals are:
%e A307299   [0]
%e A307299   [1, 1]
%e A307299   [2, 2, 2]
%e A307299   [3, 0, 3, 3]
%e A307299   [4, 4, 4, 0, 4]
%e A307299   [5, 5, 5, 5, 5, 5]
%e A307299   [6, 3, 0, 1, 1, 6, 6]
%e A307299   [7, 7, 1, 2, 0, 7, 7, 7]
%e A307299   [8, 8, 8, 6, 3, 8, 3, 4, 8]
%e A307299   [9, 6, 9, 4, 7, 9, 2, 8, 9, 9]
%e A307299   [10, 10, 10, 10, 9, 10, 10, 9, 10, 10, 10]
%e A307299   [11, 11, 11, 11, 2, 3, 4, 1, 6, 6, 11, 11]
%e A307299   [12, 9, 6, 7, 12, 1, 5, 11, 7, 7, 12, 8, 12]
%e A307299   ...
%e A307299 The triangle begins:
%e A307299   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
%e A307299   [1, 2, 3, 0, 5, 6, 7, 4, 9, 10, 11, 8]
%e A307299   [2, 0, 4, 5, 1, 7, 3, 8, 10, 6, 12]
%e A307299   [3, 4, 5, 1, 0, 8, 2, 9, 6, 7]
%e A307299   [4, 5, 0, 2, 3, 9, 10, 1, 7]
%e A307299   [5, 3, 1, 6, 7, 10, 4, 11]
%e A307299   [6, 7, 8, 4, 9, 3, 5]
%e A307299   [7, 8, 9, 10, 2, 1]
%e A307299   [8, 6, 10, 11, 12]
%e A307299   [9, 10, 11, 7]
%e A307299   [10, 11, 6]
%e A307299   [11, 9]
%e A307299   [12]
%e A307299   ...
%o A307299 (PARI) \\ See Links section.
%Y A307299 Cf. A003987, A307296, A307297, A307298.
%K A307299 nonn,tabf
%O A307299 0,4
%A A307299 _N. J. A. Sloane_, Apr 12 2019