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.

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

Offset: 1

Author

Felix Fröhlich, Jul 24 2016

Keywords

• nonn

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:

B--B--W

|

B--W

|

B--W

|

B--W

|

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)?

Examples

			n=1: B--o
     |
     o
n=2: B--o  B--W
     |     |
     o     o
n=3: B--o  B--W  B--W
     |     |     |
     o     o     B--o
                 |
                 o
n=4: B--o  B--W  B--W  B--W
     |     |     |     |
     o     o     B--o  B--W
                 |     |
                 o     o
n=5: o     o     B--o  B--o  B--B--o
     |     |     |     |     |  |
     B--o  B--o  B--o  B--W  B--W
     |     |     |     |     |
     o     W     W     W     W
n=6: o     o     o--B--o  o--B--o  B--B--o  .--.--W
     |     |     |  |     |  |     |  |     |  |
     B--o  B--o  B--o     B--W     B--W     .--W
     |     |     |        |        |        |
     o     W     W        W        W        W
		

Links

• online-go.com, Learn to play Go: Placing stones (virtual 9x9 Go board).
• Wikipedia, Go (game).

Crossrefs

Cf. A089071, A094777, A269417.