

A164950


1 if there is a winning strategy for misère Sprouts with n initial points, else 0.


2



1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1
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OFFSET

1,1


COMMENTS

This comes from changing "W" to "1" and "L" to "0" in Figure 1, p.2 of Lemoine. For the number of different canonical trees in game trees obtained from a starting position, see A164950. Sprouts is a twoplayer topological game, invented in 1967 by Michael Paterson and John Conway. The game starts with p spots, lasts at most 3p1 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.
Lemoine & Viennot conjecture that, for n > 4, a(n) = 1 if and only if n is 0, 4, or 5 mod 6.  Charles R Greathouse IV, Dec 13 2012


REFERENCES

D. Applegate, G. Jacobson, and D. Sleator, Computer Analysis of Sprouts, Tech. Report CMUCS91144, 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.
Martin Gardner, Mathematical games : of sprouts and brussels sprouts, games with a topological flavor, Scientific American 217 (July 1967), 112115.


LINKS

Table of n, a(n) for n=1..17.
Julien Lemoine, Simon Viennot, Analysis of misère Sprouts game with reduced canonical trees, Aug 30, 2009.


CROSSREFS

Cf. A164950.
Sequence in context: A159638 A187615 A120528 * A068433 A088592 A029692
Adjacent sequences: A164947 A164948 A164949 * A164951 A164952 A164953


KEYWORD

nonn,hard


AUTHOR

Jonathan Vos Post, Sep 01 2009


STATUS

approved



