

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.


1



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, 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, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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:
BBW

BW

BW

BW

o
What is the asymptotic behavior of this sequence?
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)?


LINKS



EXAMPLE

n=1: Bo

o
n=2: Bo BW
 
o o
n=3: Bo BW BW
  
o o Bo

o
n=4: Bo BW BW BW
   
o o Bo BW
 
o o
n=5: o o Bo Bo BBo
     
Bo Bo Bo BW BW
    
o W W W W
n=6: o o oBo oBo BBo ..W
         
Bo Bo Bo BW BW .W
     
o W W W W W


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



