A241985 The number of P-positions in the At-Most-2-Jars game with up to three piles, allowing for piles of zero, that are born in generation n.

1, 7, 13, 13, 25, 37, 37, 43, 37, 43, 55, 49, 73, 79, 79, 109, 97, 115, 85, 97, 97, 145, 121, 109, 163, 151, 151, 115, 121, 181, 175, 211, 193, 193, 211, 169, 211, 271, 187, 181

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.

a(n) is always 1 greater than a multiple of 6.

Examples

			For n = 1 the a(1) = 7 P-positions are (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. A241986 (first differences), A237711 (Nim), A241983 (Cookie Monster Game), A241987 (Consecutive Game).