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<DIV><FONT face="MS UI Gothic" size=2> Hello
Seqfans.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT size=2> </FONT><A
href="http://www.research.att.com/projects/OEIS?Anum=A089243"><FONT
size=2>http://www.research.att.com/projects/OEIS?Anum=A089243</FONT></A><BR></DIV>
<DIV><FONT size=2> >
0,1,3,4,9,22,55<BR></FONT><FONT face="MS UI Gothic" size=2> I
want to know more terms of this
sequence.<BR> <BR></FONT><FONT face="MS UI Gothic"
size=2></FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> Once, I tried
to calculate number of partitions into strokes of grid graph n x
n.</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> 1 x 1
<BR> .__.<BR> |__| </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> Names of
nodes<BR> 12<BR> 43</FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV>
<DIV><FONT face="MS UI Gothic" size=2> Partitions into strokes
: 12341, 1234+14, 123+143, 12+32+14+34, so b(1)=4 </FONT></DIV>
<DIV><FONT face="MS UI Gothic" size=2></FONT> </DIV><FONT
face="MS UI Gothic" size=2>
<DIV><BR> 2 x 2<BR>
.__.__.<BR> |__|__| <BR> |__|__|
</DIV>
<DIV> </DIV>
<DIV> Names of nodes<BR>
123<BR> 456<BR> 789</DIV>
<DIV> </DIV>
<DIV> In this case, a partitions like 1236987458+14+25+5*
exists. b(2)=?<BR> If n=2 then it already becomes rather
difficult. </DIV>
<DIV> </DIV>
<DIV> I also want to know about b(n)
sequence.<BR> Does anyone have a good idea to search all the
partitions into strokes?</DIV>
<DIV> </DIV>
<DIV> The idea "stroke" doesn't exist in graph theory, so I
think it is worth studying.</DIV>
<DIV> </DIV>
<DIV> Yasutoshi<BR>
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