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<DIV><FONT face="MS UI Gothic" size=2>
<DIV><FONT face="MS UI Gothic" size=2>
<DIV><FONT face="MS UI Gothic" size=2> I have awoken to
that the description on %N A000002 line is not good.
<DIV> I fixed a node, and I counted all maximal directed
paths from it.</DIV>
<DIV> And I supposed that the maximal directed paths from the
other nodes are rotations or reflections of the first paths.</DIV>
<DIV> So, I defined the sequence as %N line.</DIV>
<DIV> </DIV>
<DIV> But, for example, the case n=1: </DIV>
<DIV> .__.</DIV>
<DIV> |__|</DIV>
<DIV> Names</DIV>
<DIV> 12</DIV>
<DIV> 34 </DIV>
<DIV> Two maximal directed from
the node 1 exist.</DIV>
<DIV> They are 12431 and
13421. So, a(1)=2.</DIV>
<DIV> If the definition is
true then, 12431 is a rotation of 24312, and 24312 is a reflection of 13421. So,
12431 = 13421. It means a(1)=1.</DIV>
<DIV> </DIV>
<DIV> How should I define the sequence? </DIV>
<DIV> </DIV>
<DIV> Yasutoshi</DIV>
<DIV> </DIV></FONT></DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt MS UI Gothic">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt MS UI Gothic; font-color: black"><B>From:</B>
<A title=zbi74583@boat.zero.ad.jp href="">kohmoto</A> </DIV>
<DIV style="FONT: 10pt MS UI Gothic"><B>To:</B> <A title=seqfan@ext.jussieu.fr
href="">seqfan@ext.jussieu.fr</A> </DIV>
<DIV style="FONT: 10pt MS UI Gothic"><B>Sent:</B> Thursday, October 06, 2005
4:06 PM</DIV>
<DIV style="FONT: 10pt MS UI Gothic"><B>Subject:</B> Maximal directed
path</DIV>
<DIV><BR></DIV>
<DIV><FONT face="MS UI Gothic" size=2>
<DIV><FONT face="MS UI Gothic" size=2>
<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></BLOCKQUOTE></FONT></DIV></FONT></DIV></BODY></HTML>