A241985 The number of P-positions in the At-Most-2-Jars game with up to three piles, allowing for piles of zero, that are born in generation n.

1, 7, 13, 13, 25, 37, 37, 43, 37, 43, 55, 49, 73, 79, 79, 109, 97, 115, 85, 97, 97, 145, 121, 109, 163, 151, 151, 115, 121, 181, 175, 211, 193, 193, 211, 169, 211, 271, 187, 181

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.

a(n) is always 1 greater than a multiple of 6.

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) = 7 P-positions are (1,1,1) and permutations of (0,1,2).

Crossrefs

Cf. A241986 (first differences), A237711 (Nim), A241983 (Cookie Monster Game), A241987 (Consecutive Game).

Sequence in context: A090229 A259222 A204713 * A194408 A376298 A057930

Adjacent sequences: A241982 A241983 A241984 * A241986 A241987 A241988

Keyword

nonn

Author

Tanya Khovanova and Joshua Xiong, Aug 10 2014

Status

approved