A307302 Array read by antidiagonals: Sprague-Grundy values for the game NimHof with rules [1,0], [3,3], [0,1].

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, 0, 0, 7, 7, 7, 8, 6, 4, 6, 1, 6, 4, 6, 8, 9, 9, 5, 5, 2, 2, 5, 5, 9, 9, 10, 8, 10, 8, 3, 1, 3, 8, 10, 8, 10, 11, 11, 11, 7, 9, 0, 0, 9, 7, 11, 11, 11, 12, 10, 8

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

Table of n, a(n) for n=0..80.

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 A307302

N. J. A. Sloane, Maple program for NimHof sequences

Example

The initial antidiagonals are:
[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, 0, 0, 7, 7, 7]
[8, 6, 4, 6, 1, 6, 4, 6, 8]
[9, 9, 5, 5, 2, 2, 5, 5, 9, 9]
[10, 8, 10, 8, 3, 1, 3, 8, 10, 8, 10]
[11, 11, 11, 7, 9, 0, 0, 9, 7, 11, 11, 11]
[12, 10, 8, 10, 11, 3, 1, 3, 11, 10, 8, 10, 12]
The triangle begins:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
[1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10]
[2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8]
[3, 2, 1, 4, 0, 6, 5, 8, 7, 10]
[4, 5, 6, 0, 1, 2, 3, 9, 11]
[5, 4, 7, 6, 2, 1, 0, 3]
[6, 7, 4, 5, 3, 0, 1]
[7, 6, 5, 8, 9, 3]
[8, 9, 10, 7, 11]
[9, 8, 11, 10]
[10, 11, 8]
[11, 10]
[12]
...

Prog

(PARI) See Links section.

Crossrefs

Cf. A003987, A307296, A307297.

Sequence in context: A332448 A321132 A003987 * A307297 A307301 A307300

Adjacent sequences: A307299 A307300 A307301 * A307303 A307304 A307305

Keyword

nonn,tabf

Author

N. J. A. Sloane, Apr 13 2019

Status

approved