# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a275346 Showing 1-1 of 1 %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, Learn to play Go: Placing stones (virtual 9x9 Go board). %H A275346 Wikipedia, Go (game). %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE