A164951 Number of different canonical trees in game trees obtained from a starting position with n initial points in misere Sprouts.

10, 55, 713, 10461, 150147

Offset

2,1

Comments

From Figure 9, p.14 of Lemoine. For whether or not there is a winning strategy obtained from a starting position with n points, see A164950. Sprouts is a two-player topological game, invented in 1967 by Michael Paterson and John Conway. The game starts with p spots, lasts at most 3p-1 moves, and the player who makes the last move wins. In the misere version of Sprouts, on the contrary, the player who makes the last move loses.

References

D. Applegate, G. Jacobson, and D. Sleator, Computer Analysis of Sprouts, Tech. Report CMU-CS-91-144, Carnegie Mellon University Computer Science Technical Report, 1991.

Elwyn Berkelamp, John Conway, and Richard Guy, Winning ways for your mathematical plays, A K Peters, 2001.

Links

Table of n, a(n) for n=2..6.

Martin Gardner, Mathematical games: Of sprouts and brussels sprouts, games with a topological flavor, Scientific American 217 (July 1967), 112-115.

Julien Lemoine and Simon Viennot, Analysis of misere Sprouts game with reduced canonical trees, arXiv:0908.4407 [math.CO], 2009.

Crossrefs

Cf. A164950.

Sequence in context: A001557 A367938 A197357 * A244303 A261848 A000814

Adjacent sequences: A164948 A164949 A164950 * A164952 A164953 A164954

Keyword

nonn,more

Author

Jonathan Vos Post, Sep 01 2009

Status

approved