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<DIV><FONT face="MS UI Gothic" size=2>
Hi, Seqfans.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> I counted number of
maximal directed paths on Bridge graph which is easier than Grid
graph.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2> </FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> %I
A000001<BR> %S A000001 1, 4, 7, 9, 11<BR> %N
A000001 Length of maximal directed path on Bridge Graph
B_n.<BR> %C A000001 B_n is a graph like this :
<BR>
.__.__.__.__.__.<BR>
|__|__|__|__|__|<BR>
n squares are connected</FONT><FONT face="MS UI Gothic" size=2>. It is the
case of
n=5.<BR>
If 1<n then a(n)=2*n+3 </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV><FONT
face="MS UI Gothic" size=2>
<DIV><BR> %a A000001
n=4
<BR>
.__.__.__.__.<BR>
|__|__|__|__|<BR>
Names of
nodes<BR>
1 2 3 4
5<BR>
a b c d
e<BR>
a.g.<BR>
345edcba123c is a maximal directed path. So, a(4)=11 <BR> %Y
A000001 A000002, A049486 <BR> %K A000001 none
<BR> %O A000001 0,2 <BR> %A A000001
Yasutsohi Kohmoto </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> %I A000002<BR> %S A000002 1, 2, 6,
10<BR> %N A000002 Number of maximal directed path on Bridge
Graph B_n.</DIV>
<DIV>
Two directed paths are considered the same if one is a rotation or reflection of
the other.</DIV>
<DIV> %C A000002 B_n is a graph like this :
<BR>
.__.__.__.__.__.<BR>
|__|__|__|__|__|<BR>
n squares are connected. It is the case of n=5.</DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> </DIV>
<DIV> %a A000002
n=3
<BR>
.__.__.__.<BR>
|__|__|__|<BR>
Names of
nodes<BR>
1 2 3
4<BR>
a b c
d<BR>
Maximal directed
paths.<BR>
34dcba123c<BR>
34dc32ba12<BR>
34dc321ab2<BR>
34dc321abc<BR>
3cd432ba12<BR>
3cd4321ab2<BR>
3cd4321abc<BR>
3cba1234dc<BR>
321abc34dc<BR>
321abcd43c </DIV>
<DIV>
So, n(3)=10<BR> %Y A000002 A000001,
A089243 <BR> %K A000002
none<BR> %O A000002 0,2<BR> %A A000002
Yasutsohi Kohmoto <BR> </DIV>
<DIV> Yasutoshi</DIV>
<DIV> </DIV></FONT></FONT></DIV></FONT></DIV></BODY></HTML>