A241985 - OEIS

%I #13 Oct 06 2014 23:02:16

%S 1,7,13,13,25,37,37,43,37,43,55,49,73,79,79,109,97,115,85,97,97,145,

%T 121,109,163,151,151,115,121,181,175,211,193,193,211,169,211,271,187,

%U 181

%N 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.

%C 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.

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

%H T. Khovanova and J. Xiong, <a href="http://arxiv.org/abs/1407.1533">Cookie Monster Plays Games</a>, arXiv:1407.1533 [math.HO], 2014.

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

%Y Cf. A241986 (first differences), A237711 (Nim), A241983 (Cookie Monster Game), A241987 (Consecutive Game).

%K nonn

%O 0,2

%A _Tanya Khovanova_ and _Joshua Xiong_, Aug 10 2014