Maximal directed path

[kohmoto]

    I have awoken to that the description on %N A000002 line is not good.
    I fixed a node, and I counted all maximal directed paths from it.
    And I supposed that the maximal directed paths from the other nodes are 
rotations or reflections of the first paths.
    So, I defined the sequence as %N line.

    But, for example, the case n=1:
         .__.
         |__|
         Names
         12
         34
         Two maximal directed from the node 1 exist.
         They are 12431 and 13421. So, a(1)=2.
         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.

    How should I define the sequence?

    Yasutoshi

  ----- Original Message ----- 
  From: kohmoto
  To: seqfan at ext.jussieu.fr
  Sent: Thursday, October 06, 2005 4:06 PM
  Subject: Maximal directed path


      Hi, Seqfans.
      I counted number of maximal directed paths on Bridge graph which is 
easier than Grid graph.

      %I A000001
      %S A000001 1, 4, 7, 9, 11
      %N A000001 Length of maximal directed path on Bridge Graph B_n.
      %C A000001 B_n is a graph like this :
                           .__.__.__.__.__.
                           |__|__|__|__|__|
                           n squares are connected. It is the case of n=5.
                           If 1<n then a(n)=2*n+3


      %a A000001      n=4
                           .__.__.__.__.
                           |__|__|__|__|
                           Names of nodes
                           1 2 3 4 5
                           a b c d e
                           a.g.
                           345edcba123c is a maximal directed path. So, 
a(4)=11
      %Y A000001 A000002, A049486
      %K A000001 none
      %O A000001 0,2
      %A A000001 Yasutsohi Kohmoto



      %I A000002
      %S A000002 1, 2, 6, 10
      %N A000002 Number of maximal directed path on Bridge Graph B_n.
                         Two directed paths are considered the same if one 
is a rotation or reflection of the other.
      %C A000002 B_n is a graph like this :
                           .__.__.__.__.__.
                           |__|__|__|__|__|
                           n squares are connected. It is the case of n=5.



      %a A000002      n=3
                           .__.__.__.
                           |__|__|__|
                           Names of nodes
                           1 2 3 4
                           a b c d
                           Maximal directed paths.
                           34dcba123c
                           34dc32ba12
                           34dc321ab2
                           34dc321abc
                           3cd432ba12
                           3cd4321ab2
                           3cd4321abc
                           3cba1234dc
                           321abc34dc
                           321abcd43c
                           So, n(3)=10
      %Y A000002 A000001, A089243
      %K A000002 none
      %O A000002 0,2
      %A A000002 Yasutsohi Kohmoto

      Yasutoshi
 
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