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.

1, 8, 21, 34, 59, 96, 133, 176, 213, 256, 311, 360, 433, 512, 591, 700, 797, 912, 997, 1094, 1191, 1336, 1457, 1566, 1729, 1880, 2031, 2146, 2267, 2448, 2623, 2834, 3027, 3220, 3431, 3600, 3811, 4082, 4269, 4450

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..39.

T. Khovanova and J. Xiong, Cookie Monster Plays Games, arXiv:1407.1533 [math.HO], 2014.

Example

For n = 1 the a(1) = 8 P-positions are (0,0,0), (1,1,1), and permutations of (0,1,2).

Crossrefs

Cf. A241985 (partial sums), A237686 (Nim), A241984 (Cookie Monster Game), A241988 (Consecutive Game).

Sequence in context: A090206 A139590 A154894 * A179681 A224039 A279895

Adjacent sequences: A241983 A241984 A241985 * A241987 A241988 A241989

Keyword

nonn

Author

Tanya Khovanova and Joshua Xiong, Aug 10 2014

Status

approved