A241988 The number of P-positions in the Consecutive game with at most three piles, allowing for piles of zero, that are born by generation n.

1, 6, 15, 28, 41, 64, 93, 122, 151, 190, 229, 276, 337, 394, 445, 508, 581, 660, 741, 820, 903, 996, 1083, 1170, 1275, 1372, 1467, 1590, 1711, 1848, 1977, 2088, 2213, 2358, 2489, 2648, 2801, 2972, 3133, 3306

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.

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) = 6 P-positions are (0,0,0), (1,0,1), (0,1,2), (0,2,1), (1,2,0), and (2,1,0).

Crossrefs

Cf. A241987 (partial sums), A237686 (Nim), A241984 (Cookie Monster Game), A241986 (At-Most-2-Jars Game).

Sequence in context: A161777 A117519 A091012 * A058008 A094142 A081873

Adjacent sequences: A241985 A241986 A241987 * A241989 A241990 A241991

Keyword

nonn

Author

Tanya Khovanova and Joshua Xiong, Aug 10 2014

Status

approved