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%I #16 Dec 11 2015 22:01:23
%S 1,7,19,37,55,82,127,166,232,316,385,463,547,634,706,805,922,1036,
%T 1165,1294,1429,1597,1735,1888,2041,2203,2395,2596,2749,2911,3133,
%U 3337,3559,3772,4009,4261,4489,4723,4987,5242
%N 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.
%C 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.
%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 (0,0,0) and (0,1,2), and permutations.
%Y Cf. A241983 (partial sums), A237686 (Nim), A241986 (At-Most-2-Jars Game), A241988 (Consecutive Game).
%K nonn
%O 0,2
%A _Tanya Khovanova_ and _Joshua Xiong_, Aug 10 2014
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