A241984 The number of P-positions in the Cookie Monster game with at most three piles, allowing for piles of zero, that are born by generation n.

1, 7, 19, 37, 55, 82, 127, 166, 232, 316, 385, 463, 547, 634, 706, 805, 922, 1036, 1165, 1294, 1429, 1597, 1735, 1888, 2041, 2203, 2395, 2596, 2749, 2911, 3133, 3337, 3559, 3772, 4009, 4261, 4489, 4723, 4987, 5242

Offset: 0

Author

Tanya Khovanova and Joshua Xiong, Aug 10 2014

Keywords

• nonn

Comments

In the Cookie Monster game, there are several piles of counters. A player is allowed to take the same positive number of counters from any nonempty subset of the piles. The player who cannot move loses.

Examples

			For n = 1 the a(1) = 7 P-positions are (0,0,0) and (0,1,2), and permutations.
		

Links

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

Crossrefs

Cf. A241983 (partial sums), A237686 (Nim), A241986 (At-Most-2-Jars Game), A241988 (Consecutive Game).