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

0,3

Comments

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

If we add 1 to every term we get A274630.

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

Example

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, ...
  ...

Prog

(PARI) See Links section.

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).

Sequence in context: A194459 A143120 A353277 * A026362 A223490 A354749

Adjacent sequences: A308198 A308199 A308200 * A308202 A308203 A308204

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jun 30 2019

Extensions

More terms from Rémy Sigrist, Jun 30 2019

Status

approved