A308201 Sprague-Grundy values for Maharaja Nim on an infinite single-quadrant board scanned by upwards antidiagonals.

0, 1, 2, 3, 4, 5, 2, 6, 7, 1, 4, 0, 8, 3, 6, 5, 1, 9, 10, 0, 4, 6, 3, 11, 5, 2, 8, 7, 7, 8, 10, 12, 1, 9, 5, 3, 9, 11, 0, 2, 3, 6, 12, 10, 8, 8, 5, 1, 4, 7, 0, 11, 13, 2, 9, 10, 12, 2, 6, 5, 13, 8, 4, 0, 11, 14, 11, 7, 3, 13, 8, 10, 9, 2, 14, 1, 6, 12, 12, 9

Offset: 0

Author

N. J. A. Sloane, Jun 30 2019

Keywords

• nonn
• tabl

Comments

A Maharaja combines the moves of a queen and a knight.

If we add 1 to every term we get A274630.

Examples

			The Sprague-Grundy values are as follows (this shows the first 7 antidiagonals):
  0,  2,  5,  1,  6,  4,  7, ...
  1,  4,  7,  3,  0,  8, ...
  3,  6,  8, 10,  2, ...
  2,  0,  9,  5, ...
  4,  1, 11, ...
  5,  3, ...
  6, ...
  ...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10010
• Urban Larsson and Johan Wästlund, Maharaja Nim: Wythoff’s Queen meets the Knight, arXiv 1207.0765 [math.CO], 2012.
• Urban Larsson and Johan Wästlund, Maharaja Nim: Wythoff’s Queen meets the Knight, Integers: Electronic Journal of Combinatorial Number Theory 14 (2014), #G05.
• Rémy Sigrist, Colored representation of the first 1000 antidiagonals (where the hue is function of T(x,y) and black pixels correspond to 0's)
• Rémy Sigrist, PARI program for A308201

Crossrefs

Cf. A307282.

For the positions of the 0's, see A307281.

The top row of the array is A308882 (or A274632 - 1).

The leading column is A274631 - 1, the main diagonal is A274633 - 1.

A274630 is essentially the same sequence (but with 1 added to every term).

Programs

PARI

See Links section.

Extensions

More terms from Rémy Sigrist, Jun 30 2019