A305384 Square array read by antidiagonals: T(i,j) = Sprague-Grundy function for position (i,j) in the "E" variant of Wythoff's game.

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

Offset

0,4

Links

Robert Price, Table of n, a(n) for n = 0..20300

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,
4,4,3,4,4,
5,5,5,5,5,5,
6,3,1,6,1,3,6,
7,7,6,7,7,6,7,7,
8,8,8,0,8,0,8,8,8,
...
The square array begins:
...
9.. 9 10 11 12 2 1 15 16 17 18
8.. 8 6 9 10 11 13 14 15 16 17
7.. 7 8 4 2 0 12 13 14 15 16
6.. 6 7 8 1 10 11 12 13 14 15
5.. 5 3 6 0 9 10 11 12 13 1
4.. 4 5 1 7 8 9 10 0 11 2
3.. 3 4 5 6 7 0 1 2 10 12
2.. 2 0 3 5 1 6 8 4 9 11
1.. 1 2 0 4 5 3 7 8 6 10
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. A305383.

Sequence in context: A004481 A307296 A004489 * A112599 A347905 A308119

Adjacent sequences: A305381 A305382 A305383 * A305385 A305386 A305387

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jun 21 2018

Extensions

More terms from Robert Price, Jul 12 2018

Status

approved