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A275346 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.

%I A275346 #25 Jul 07 2018 15:46:30
%S A275346 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 A275346 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 A275346 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1
%N A275346 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 A275346 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 A275346 B--B--W
%C A275346 |
%C A275346 B--W
%C A275346 |
%C A275346 B--W
%C A275346 |
%C A275346 B--W
%C A275346 |
%C A275346 o
%C A275346 What is the asymptotic behavior of this sequence?
%C A275346 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 A275346 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 A275346 Wikipedia, <a href="https://en.wikipedia.org/wiki/Go_(game)">Go (game)</a>.
%e A275346 n=1: B--o
%e A275346      |
%e A275346      o
%e A275346 n=2: B--o  B--W
%e A275346      |     |
%e A275346      o     o
%e A275346 n=3: B--o  B--W  B--W
%e A275346      |     |     |
%e A275346      o     o     B--o
%e A275346                  |
%e A275346                  o
%e A275346 n=4: B--o  B--W  B--W  B--W
%e A275346      |     |     |     |
%e A275346      o     o     B--o  B--W
%e A275346                  |     |
%e A275346                  o     o
%e A275346 n=5: o     o     B--o  B--o  B--B--o
%e A275346      |     |     |     |     |  |
%e A275346      B--o  B--o  B--o  B--W  B--W
%e A275346      |     |     |     |     |
%e A275346      o     W     W     W     W
%e A275346 n=6: o     o     o--B--o  o--B--o  B--B--o  .--.--W
%e A275346      |     |     |  |     |  |     |  |     |  |
%e A275346      B--o  B--o  B--o     B--W     B--W     .--W
%e A275346      |     |     |        |        |        |
%e A275346      o     W     W        W        W        W
%Y A275346 Cf. A089071, A094777, A269417.
%K A275346 nonn
%O A275346 1,1
%A A275346 _Felix Fröhlich_, Jul 24 2016