A305383 Square array read by antidiagonals: T(i,j) = Sprague-Grundy function for position (i,j) in the "R" variant of Wythoff's game.

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

Offset

0,4

Links

Robert Price, Table of n, a(n) for n = 0..45450

Nhan Bao Ho, Two variants of Wythoff's game preserving its P-positions, Journal of Combinatorial Theory, Series A, Volume 119, Issue 6, August 2012, pp. 1302-1314.

Example

The first few antidiagonals are:
0,
1,1,
2,2,2,
3,0,0,3,
4,3,1,3,4,
5,4,3,3,4,5,
6,5,4,4,4,5,6,
7,6,5,2,2,5,6,7,
8,7,6,0,3,0,6,7,8,
...
The square array begins:
...
9....9 9 9 5 9 1 9 5 9 10
8....8 8 8 8 8 2 8 6 7 9
7....7 7 7 7 0 7 7 8 6 5
6....6 6 6 1 1 4 5 7 8 9
5....5 5 5 0 5 6 4 7 2 1
4....4 4 4 2 3 5 1 0 8 9
3....3 3 3 4 2 0 1 7 8 5
2....2 0 1 3 4 5 6 7 8 9
1....1 2 0 3 4 5 6 7 8 9
0....0 1 2 3 4 5 6 7 8 9
a/b. 0 1 2 3 4 5 6 7 8 9

Crossrefs

Cf. A305384.

Sequence in context: A343471 A035307 A292373 * A004481 A307296 A004489

Adjacent sequences: A305380 A305381 A305382 * A305384 A305385 A305386

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jun 21 2018

Extensions

More terms from Robert Price, Jul 12 2018

Status

approved