A241984 The number of P-positions in the Cookie Monster game with at most three piles, allowing for piles of zero, that are born by generation n.

1, 7, 19, 37, 55, 82, 127, 166, 232, 316, 385, 463, 547, 634, 706, 805, 922, 1036, 1165, 1294, 1429, 1597, 1735, 1888, 2041, 2203, 2395, 2596, 2749, 2911, 3133, 3337, 3559, 3772, 4009, 4261, 4489, 4723, 4987, 5242

Offset

0,2

Comments

In the Cookie Monster game, there are several piles of counters. A player is allowed to take the same positive number of counters from any nonempty subset of the piles. 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) = 7 P-positions are (0,0,0) and (0,1,2), and permutations.

Crossrefs

Cf. A241983 (partial sums), A237686 (Nim), A241986 (At-Most-2-Jars Game), A241988 (Consecutive Game).

Sequence in context: A192594 A352243 A031337 * A301717 A152540 A073859

Adjacent sequences: A241981 A241982 A241983 * A241985 A241986 A241987

Keyword

nonn

Author

Tanya Khovanova and Joshua Xiong, Aug 10 2014

Status

approved