Maximal directed path

[kohmoto]

    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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