A307301 - OEIS

%I #12 Apr 13 2019 22:18:48

%S 0,1,1,2,0,2,3,3,3,3,4,2,0,2,4,5,5,4,1,5,5,6,4,1,0,6,4,6,7,7,6,6,1,7,

%T 7,7,8,6,5,7,0,6,4,6,8,9,9,8,8,2,2,8,5,9,9,10,8,7,4,3,0,3,9,10,8,10,

%U 11,11,10,5,9,9,1,8,5,11,11,11,12,10,9,11

%N Array read by antidiagonals: Sprague-Grundy values for the game NimHof with rules [1,0], [3,1], [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="/A307301/a307301.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="/A307301/a307301.gp.txt">PARI program for A307301</a>

%H N. J. A. Sloane, <a href="/A307296/a307296.txt">Maple program for NimHof sequences</a>

%e The initial antidiagonals are:

%e [0]

%e [1, 1]

%e [2, 0, 2]

%e [3, 3, 3, 3]

%e [4, 2, 0, 2, 4]

%e [5, 5, 4, 1, 5, 5]

%e [6, 4, 1, 0, 6, 4, 6]

%e [7, 7, 6, 6, 1, 7, 7, 7]

%e [8, 6, 5, 7, 0, 6, 4, 6, 8]

%e [9, 9, 8, 8, 2, 2, 8, 5, 9, 9]

%e [10, 8, 7, 4, 3, 0, 3, 9, 10, 8, 10]

%e [11, 11, 10, 5, 9, 9, 1, 8, 5, 11, 11, 11]

%e [12, 10, 9, 11, 10, 1, 0, 3, 7, 7, 8, 10, 12]

%e ...

%e The triangle begins:

%e [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]

%e [1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10]

%e [2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8]

%e [3, 2, 4, 0, 1, 6, 8, 9, 5, 7]

%e [4, 5, 1, 6, 0, 2, 3, 8, 7]

%e [5, 4, 6, 7, 2, 0, 1, 3]

%e [6, 7, 5, 8, 3, 9, 0]

%e [7, 6, 8, 4, 9, 1]

%e [8, 9, 7, 5, 10]

%e [9, 8, 10, 11]

%e [10, 11, 9]

%e [11, 10]

%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 13 2019