# Connectness

koh zbi74583.boat at orange.zero.jp
Thu Jul 10 03:12:56 CEST 2008

```    Hi, Seqfans
In game of GO a kind of connectness is defined.

1. Two stones are connected if they are next each other horizontally or vertically.
2. If a stone X is connected with a stone Y and Y is connected with a stone Z then X and Z are connected.
3. Set of n stones is connected if all members of the set are connected each other.
4. Set of m stones of same color is connected if the configuration becomes connected after k steps in game of GO.

[Explanation]
1.
connected
+ o o +
or
+
o
o
+
not connected
+ o + +
+ + o +
or
+ o + o +
etc

4.
connected
+ o + +
+ + o +
Because if black player tried to cut the two stones.
+ o x +
+ + o +
White player would put a stone like this.
+ o x +
+ o o +

not connected
+ o x +
+ x o +
no way to connect them

Where "o" means white stone, "x" means black stone

I want to know number of connected configurations of stone  of same color.

S : 1,8,124....

n=1

o        1

n=2

o o      2

o +      2
+ o

o +      4
+ +
+ o

n=3

o o o    2

o o      4
+ o

o o +    8
+ + o

o + o    4
+ o +

o + +    2
+ o +
+ + o

o o + o    4

o o +     8
+ + +
+ + o

o o       8
+ +
+ o

+ o +     4
+ + o
o + +

+ + o +     8
o + + o

o + o      4
+ + +
+ + o

o o + +    8
+ + + o

o o        8
+ +
+ +
+ o

o + + o    4
+ + + +
+ + + +
+ + + o

o + o +     8
+ + + o

o + + o    8
+ + + +
+ + + +
+ + o +

o + + o    8
+ + + +
+ + + o

o + + o    8
+ + + +
+ + o +

+ + + o    8
+ + + +
o + + +
+ + o +

+ + + o    8
+ + + +
+ + + +
+ o o +

Why is the following configuration of two stones not connected?

o + o

Because

o x o

+ o +
o x o

+ o +
o x o
+ x +

o o +
o x o
+ x +

o o x
o x o
+ x +

o o x o
o x o +
+ x + +

+ + x +
o o x o
o x o +
+ x + +

+ + o +
+ + x +
o o x o
o x o +
+ x + +

No way to connect the white stones

Yasutoshi

```

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