A241987 The number of P-positions in the Consecutive game with at most three piles, allowing for piles of zero, that are born in generation n.

1, 5, 9, 13, 13, 23, 29, 29, 29, 39, 39, 47, 61, 57, 51, 63, 73, 79, 81, 79, 83, 93, 87, 87, 105, 97, 95, 123, 121, 137, 129, 111, 125, 145, 131, 159, 153, 171, 161, 173

Offset

0,2

Comments

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.

a(n) is always odd.

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) = 5 P-positions are (1,0,1), (0,1,2), (0,2,1), (1,2,0), and (2,1,0).

Crossrefs

Cf. A241988 (first differences), A237711 (Nim), A241983 (Cookie Monster Game), A241985 (At-Most-2-Jars Game).

Sequence in context: A079357 A080455 A122798 * A189464 A130333 A304868

Adjacent sequences: A241984 A241985 A241986 * A241988 A241989 A241990

Keyword

nonn

Author

Tanya Khovanova and Joshua Xiong, Aug 10 2014

Status

approved