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%I A135443 #10 May 05 2023 01:42:43
%S A135443 2,8,12,40,84,144,220,312,420,544,684,840,1012,1200,1404,1624,1860,
%T A135443 2112,2380,2664,2964,3280,3612,3960,4324,4704,5100,5512,5940,6384,
%U A135443 6844,7320,7812,8320,8844,9384,9940,10512,11100,11704,12324,12960,13612,14280
%N A135443 Number of maximal directed trails in the labeled n-ladder graph P_2 X P_n.
%F A135443 For n > 2, a(n) = 4 * (n-2) * (2*n - 3) = A033586(n-2). - _Max Alekseyev_, May 04 2023
%e A135443 For n = 4 the graph is
%e A135443   .__.__.__.
%e A135443   |__|__|__|
%e A135443 Names of nodes:
%e A135443   1 2 3 4
%e A135443   a b c d
%e A135443 Maximal directed paths which start from node 3:
%e A135443   34dcba123c
%e A135443   34dc32ba12
%e A135443   34dc321ab2
%e A135443   34dc321abc
%e A135443   3cd432ba12
%e A135443   3cd4321ab2
%e A135443   3cd4321abc
%e A135443   3cba1234dc
%e A135443   321abc34dc
%e A135443   321abcd43c
%e A135443 There are also paths from nodes c,b,2. So n(4) = 4*10 = 40.
%Y A135443 Apart from initial terms sequence is the same as A033586.
%Y A135443 Cf. A003682, A089243.
%K A135443 nonn,walk
%O A135443 1,1
%A A135443 _Yasutoshi Kohmoto_, Feb 18 2008
%E A135443 Edited and extended by _Max Alekseyev_, May 04 2023

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