OFFSET
0,4
COMMENTS
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.
REFERENCES
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?
LINKS
Rémy Sigrist, Colored representation of T(x,y) for x = 0..1023 and y = 0..1023 (where the hue is function of T(x,y) and black pixels correspond to zeros)
Rémy Sigrist, PARI program for A307299
N. J. A. Sloane, Maple program for NimHof sequences
EXAMPLE
The initial antidiagonals are:
[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, 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, 10, 10]
[11, 11, 11, 11, 2, 3, 4, 1, 6, 6, 11, 11]
[12, 9, 6, 7, 12, 1, 5, 11, 7, 7, 12, 8, 12]
...
The triangle begins:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
[1, 2, 3, 0, 5, 6, 7, 4, 9, 10, 11, 8]
[2, 0, 4, 5, 1, 7, 3, 8, 10, 6, 12]
[3, 4, 5, 1, 0, 8, 2, 9, 6, 7]
[4, 5, 0, 2, 3, 9, 10, 1, 7]
[5, 3, 1, 6, 7, 10, 4, 11]
[6, 7, 8, 4, 9, 3, 5]
[7, 8, 9, 10, 2, 1]
[8, 6, 10, 11, 12]
[9, 10, 11, 7]
[10, 11, 6]
[11, 9]
[12]
...
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Apr 12 2019
STATUS
approved