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A241986 The number of P-positions in the At-Most-2-Jars game with at most three piles, allowing for piles of zero, that are born by generation n. 3

%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 P-positions in the At-Most-2-Jars game with at most three piles, allowing for piles of zero, that are born by 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.

%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 P-positions 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

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Last modified January 21 03:58 EST 2022. Contains 350473 sequences. (Running on oeis4.)