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%I #25 Jul 07 2018 15:46:30
%S 2,1,2,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
%T 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
%U 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1
%N In Go, minimum total number of liberties player 1 (black) can have on a standard 19 X 19 board after n moves when no player passes a move, with no repeating game positions allowed.
%C For many small n, a(n) = 0 when n is even and a(n) = 1 when n is odd, because a row of black stones can be played on the outer line of the board with a row of white stones running adjacent to the black stones, as in the following diagram:
%C B--B--W
%C |
%C B--W
%C |
%C B--W
%C |
%C B--W
%C |
%C o
%C What is the asymptotic behavior of this sequence?
%C Does a(n) exist for all n or does a constant c exist such that a(n) is undefined for n >= c (because no more legal moves are possible)?
%H online-go.com, <a href="https://online-go.com/learn-to-play-go#placing-stones">Learn to play Go: Placing stones</a> (virtual 9x9 Go board).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Go_(game)">Go (game)</a>.
%e n=1: B--o
%e |
%e o
%e n=2: B--o B--W
%e | |
%e o o
%e n=3: B--o B--W B--W
%e | | |
%e o o B--o
%e |
%e o
%e n=4: B--o B--W B--W B--W
%e | | | |
%e o o B--o B--W
%e | |
%e o o
%e n=5: o o B--o B--o B--B--o
%e | | | | | |
%e B--o B--o B--o B--W B--W
%e | | | | |
%e o W W W W
%e n=6: o o o--B--o o--B--o B--B--o .--.--W
%e | | | | | | | | | |
%e B--o B--o B--o B--W B--W .--W
%e | | | | | |
%e o W W W W W
%Y Cf. A089071, A094777, A269417.
%K nonn
%O 1,1
%A _Felix Fröhlich_, Jul 24 2016
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