A241987 The number of P-positions in the Consecutive game with at most three piles, allowing for piles of zero, that are born in generation n.

1, 5, 9, 13, 13, 23, 29, 29, 29, 39, 39, 47, 61, 57, 51, 63, 73, 79, 81, 79, 83, 93, 87, 87, 105, 97, 95, 123, 121, 137, 129, 111, 125, 145, 131, 159, 153, 171, 161, 173

Offset: 0

Author

Tanya Khovanova and Joshua Xiong, Aug 10 2014

Keywords

• nonn

Comments

In the Consecutive game, there are several piles of counters. A player is allowed to take the same positive number of counters from any subset of consecutive piles or any positive number of counters from one pile. The player who cannot move loses.

a(n) is always odd.

Examples

			For n = 1 the a(1) = 5 P-positions are (1,0,1), (0,1,2), (0,2,1), (1,2,0), and (2,1,0).
		

Links

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

Crossrefs

Cf. A241988 (first differences), A237711 (Nim), A241983 (Cookie Monster Game), A241985 (At-Most-2-Jars Game).