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%I #10 Apr 01 2022 09:13:54
%S 10,55,713,10461,150147
%N Number of different canonical trees in game trees obtained from a starting position with n initial points in misere Sprouts.
%C 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.
%D 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.
%D Elwyn Berkelamp, John Conway, and Richard Guy, Winning ways for your mathematical plays, A K Peters, 2001.
%H Martin Gardner, <a href="https://www.jstor.org/stable/24926062">Mathematical games: Of sprouts and brussels sprouts, games with a topological flavor</a>, Scientific American 217 (July 1967), 112-115.
%H Julien Lemoine and Simon Viennot, <a href="http://arxiv.org/abs/0908.4407">Analysis of misere Sprouts game with reduced canonical trees</a>, arXiv:0908.4407 [math.CO], 2009.
%Y Cf. A164950.
%K nonn,more
%O 2,1
%A _Jonathan Vos Post_, Sep 01 2009
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