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%I #22 Dec 03 2024 09:04:35
%S 1,1,2,5,16,57,226,961,4376,21041,106534,563961,3112924,17839993,
%T 105907946,649432673,4105783696,26706965985,178466243662,
%U 1223248786921,8589272300516,61708802126441,453143009601682,3397715981566545,25990997059282456,202666687407866257
%N Number of maximal chains in the poset of all binary words of length <= n, ordered by B covers A iff A_i <= B_{i+k} for all i in A and some k >= 0.
%e a(3) = 5:
%e () < (0) < (0,0) < (0,0,0),
%e () < (0) < (0,0) < (0,1),
%e () < (0) < (0,0) < (1,0),
%e () < (0) < (1) < (0,1),
%e () < (0) < (1) < (1,0).
%o (Python)
%o def mchains(n, k): return # See A378588
%o def A378382_list(max_n): return mchains(max_n,2)
%Y Cf. A034841, A143672, A282698, A317145, column k=2 of A378588, A378608.
%K nonn,new
%O 0,3
%A _John Tyler Rascoe_, Nov 26 2024