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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 (list; graph; refs; listen; history; text; internal format)
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 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.

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 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.

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

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

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Last modified March 27 08:27 EDT 2017. Contains 284146 sequences.