A307296 Array read by antidiagonals: Sprague-Grundy values for the game NimHof with 4 rules [1,0], [3,2], [1,1], [0,1].
0, 1, 1, 2, 2, 2, 3, 0, 0, 3, 4, 4, 1, 4, 4, 5, 5, 5, 5, 5, 5, 6, 3, 3, 6, 3, 3, 6, 7, 7, 4, 7, 7, 4, 7, 7, 8, 8, 8, 1, 8, 0, 8, 8, 8, 9, 6, 6, 0, 2, 2, 1, 6, 6, 9, 10, 10, 7, 2, 9, 7, 9, 2, 7, 10, 10, 11, 11, 11, 9, 10, 10, 10, 0, 9, 11, 11, 11, 12, 9, 9, 12, 0, 11, 3, 11, 1, 12, 9, 9, 12
Offset: 0
Examples
The initial antidiagonals are: [0], [1, 1], [2, 2, 2], [3, 0, 0, 3], [4, 4, 1, 4, 4], [5, 5, 5, 5, 5, 5], [6, 3, 3, 6, 3, 3, 6], [7, 7, 4, 7, 7, 4, 7, 7], [8, 8, 8, 1, 8, 0, 8, 8, 8], [9, 6, 6, 0, 2, 2, 1, 6, 6, 9], [10, 10, 7, 2, 9, 7, 9, 2, 7, 10, 10], [11, 11, 11, 9, 10, 10, 10, 0, 9, 11, 11, 11], [12, 9, 9, 12, 0, 11, 3, 11, 1, 12, 9, 9, 12], The triangle begins: [1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9] [2, 0, 1, 5, 3, 4, 8, 6, 7, 11, 9] [3, 4, 5, 6, 7, 0, 1, 2, 9, 12] [4, 5, 3, 7, 8, 2, 9, 0, 1] [5, 3, 4, 1, 2, 7, 10, 11] [6, 7, 8, 0, 9, 10, 3] [7, 8, 6, 2, 10, 11] [8, 6, 7, 9, 0] [9, 10, 11, 12] [10, 11, 9] [11, 9] [12] ...
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..999 and y = 0..999 (where the hue is function of T(x,y) and black pixels correspond to zeros)
- Rémy Sigrist, PARI program for A307296
- N. J. A. Sloane, Maple program for NimHof sequences
Crossrefs
List of NimHof sequences:
A-number Rules R
A003987 [1,0], [0,1]
A004481 [1,0], [1,1], [0,1]
A003987 [1,0], [2,1], [0,1]
A307300 [1,0], [2,2], [0,1]
A307301 [1,0], [3,1], [0,1]
A003987 [1,0], [3,2], [0,1]
A307302 [1,0], [3,3], [0,1]
A307299 [1,0], [1,1], [1,2], [0,1]
A307296 [1,0], [1,1], [3,2], [0,1]
A307297 [1,0], [2,1], [3,3], [0,1]
A307298 [1,0], [1,1], [1,2], [2,3], [0,1]
Programs
-
PARI
\\ See Links section.
Comments