A241986 The number of P-positions in the At-Most-2-Jars game with at most three piles, allowing for piles of zero, that are born by generation n.

1, 8, 21, 34, 59, 96, 133, 176, 213, 256, 311, 360, 433, 512, 591, 700, 797, 912, 997, 1094, 1191, 1336, 1457, 1566, 1729, 1880, 2031, 2146, 2267, 2448, 2623, 2834, 3027, 3220, 3431, 3600, 3811, 4082, 4269, 4450

Offset: 0

Author

Tanya Khovanova and Joshua Xiong, Aug 10 2014

Keywords

• nonn

Comments

In the At-Most-2-Jars game, there are several piles of counters. A player is allowed to take the same positive number of counters from any subset of two piles or any positive number of counters from one pile. The player who cannot move loses.

Examples

			For n = 1 the a(1) = 8 P-positions are (0,0,0), (1,1,1), and permutations of (0,1,2).
		

Links

• T. Khovanova and J. Xiong, Cookie Monster Plays Games, arXiv:1407.1533 [math.HO], 2014.

Crossrefs

Cf. A241985 (partial sums), A237686 (Nim), A241984 (Cookie Monster Game), A241988 (Consecutive Game).