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A135443 Number of maximal directed trails in the labeled n-ladder graph P_2 X P_n. 0

%I #10 May 05 2023 01:42:43

%S 2,8,12,40,84,144,220,312,420,544,684,840,1012,1200,1404,1624,1860,

%T 2112,2380,2664,2964,3280,3612,3960,4324,4704,5100,5512,5940,6384,

%U 6844,7320,7812,8320,8844,9384,9940,10512,11100,11704,12324,12960,13612,14280

%N Number of maximal directed trails in the labeled n-ladder graph P_2 X P_n.

%F For n > 2, a(n) = 4 * (n-2) * (2*n - 3) = A033586(n-2). - _Max Alekseyev_, May 04 2023

%e For n = 4 the graph is

%e .__.__.__.

%e |__|__|__|

%e Names of nodes:

%e 1 2 3 4

%e a b c d

%e Maximal directed paths which start from node 3:

%e 34dcba123c

%e 34dc32ba12

%e 34dc321ab2

%e 34dc321abc

%e 3cd432ba12

%e 3cd4321ab2

%e 3cd4321abc

%e 3cba1234dc

%e 321abc34dc

%e 321abcd43c

%e There are also paths from nodes c,b,2. So n(4) = 4*10 = 40.

%Y Apart from initial terms sequence is the same as A033586.

%Y Cf. A003682, A089243.

%K nonn,walk

%O 1,1

%A _Yasutoshi Kohmoto_, Feb 18 2008

%E Edited and extended by _Max Alekseyev_, May 04 2023

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Last modified June 16 10:42 EDT 2024. Contains 373425 sequences. (Running on oeis4.)