

A241988


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


3



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
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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 Ppositions 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 (AtMost2Jars 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



