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%I #13 Oct 06 2014 23:02:43
%S 1,6,15,28,41,64,93,122,151,190,229,276,337,394,445,508,581,660,741,
%T 820,903,996,1083,1170,1275,1372,1467,1590,1711,1848,1977,2088,2213,
%U 2358,2489,2648,2801,2972,3133,3306
%N The number of P-positions in the Consecutive game with at most three piles, allowing for piles of zero, that are born by generation n.
%C 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.
%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) = 6 P-positions are (0,0,0), (1,0,1), (0,1,2), (0,2,1), (1,2,0), and (2,1,0).
%Y Cf. A241987 (partial sums), A237686 (Nim), A241984 (Cookie Monster Game), A241986 (At-Most-2-Jars Game).
%K nonn
%O 0,2
%A _Tanya Khovanova_ and _Joshua Xiong_, Aug 10 2014
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