%I
%S 1,8,21,34,59,96,133,176,213,256,311,360,433,512,591,700,797,912,997,
%T 1094,1191,1336,1457,1566,1729,1880,2031,2146,2267,2448,2623,2834,
%U 3027,3220,3431,3600,3811,4082,4269,4450
%N The number of Ppositions in the AtMost2Jars game with at most three piles, allowing for piles of zero, that are born by generation n.
%C In the AtMost2Jars 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.
%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) = 8 Ppositions are (0,0,0), (1,1,1), and permutations of (0,1,2).
%Y Cf. A241985 (partial sums), A237686 (Nim), A241984 (Cookie Monster Game), A241988 (Consecutive Game).
%K nonn
%O 0,2
%A _Tanya Khovanova_ and _Joshua Xiong_, Aug 10 2014
