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

1,1

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:

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)?

Links

Table of n, a(n) for n=1..87.

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

Wikipedia, Go (game).

Example

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

Crossrefs

Cf. A089071, A094777, A269417.

Sequence in context: A039924 A349218 A364205 * A037888 A052308 A116510

Adjacent sequences: A275343 A275344 A275345 * A275347 A275348 A275349

Keyword

nonn

Author

Felix Fröhlich, Jul 24 2016

Status

approved