Maximal directed path

[kohmoto]

    Neil
    I rewrote A000002.
    I am sure that the definition became better.

    Yasutoshi




    %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 2, 8, 12, 40
    %N A000002 Number of maximal directed path on Bridge Graph B_n.
    %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 which start from node 3.
                         34dcba123c
                         34dc32ba12
                         34dc321ab2
                         34dc321abc
                         3cd432ba12
                         3cd4321ab2
                         3cd4321abc
                         3cba1234dc
                         321abc34dc
                         321abcd43c
                         Paths from nodes c,b,2 exist.
                         So, n(3)=4*10=40
    %Y A000002 A000001, A089243
    %K A000002 none
    %O A000002 0,1
    %A A000002 Yasutsohi Kohmoto

  ----- 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
 
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20051025/3b8826aa/attachment-0001.htm>