A378588 -id:A378588 - cp's OEIS frontend

A378382 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.

1, 1, 2, 5, 16, 57, 226, 961, 4376, 21041, 106534, 563961, 3112924, 17839993, 105907946, 649432673, 4105783696, 26706965985, 178466243662, 1223248786921, 8589272300516, 61708802126441, 453143009601682, 3397715981566545, 25990997059282456, 202666687407866257

Offset: 0

John Tyler Rascoe, Nov 26 2024

nonn

			a(3) = 5:
 () < (0) < (0,0) < (0,0,0),
 () < (0) < (0,0) < (0,1),
 () < (0) < (0,0) < (1,0),
 () < (0) < (1) < (0,1),
 () < (0) < (1) < (1,0).

Cf. A034841, A143672, A282698, A317145, column k=2 of A378588, A378608.

def mchains(n, k): return # See A378588
def A378382_list(max_n): return mchains(max_n,2)

A378608 Number of maximal chains in the poset of all n-ary words of length <= n, ordered by B covers A iff A_i <= B_{i+k} for all i in A and some k >= 0.

Original entry on oeis.org

1, 1, 2, 6, 23, 103, 518, 2868, 17263, 111925, 775994, 5719338, 44592007, 366259499, 3157877470, 28492791496, 268307662047, 2630577754281, 26795670672626, 283038010150702, 3094882721541239, 34977231456293519, 407991690851302646, 4905431774834649852, 60721792897771836879

Offset: 0

John Tyler Rascoe, Dec 01 2024

nonn

			a(3) = 6:
  () < (1) < (1,1) < (1,1,1),
  () < (1) < (1,1) < (1,2),
  () < (1) < (1,1) < (2,1),
  () < (1) < (2) < (1,2),
  () < (1) < (2) < (2,1),
  () < (1) < (2) < (3).

Cf. A034841, A143672, A282698, A317145, A378382, main diagonal of A378588.

def mchains(n,k): return # See A378588
def A378608_list(max_n): return mchains(max_n,max_n)

cp's OEIS Frontend

A378382 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.

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