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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. 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:

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: A093654 A220115 A039924 * A037888 A052308 A116510

Adjacent sequences:  A275343 A275344 A275345 * A275347 A275348 A275349

KEYWORD

nonn

AUTHOR

Felix Fröhlich, Jul 24 2016

STATUS

approved

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Last modified November 25 19:43 EST 2020. Contains 338625 sequences. (Running on oeis4.)