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.

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

0,3

Links

Table of n, a(n) for n=0..24.

Example

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).

Prog

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

Crossrefs

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

Sequence in context: A374547 A263778 A352854 * A053488 A338279 A117106

Adjacent sequences: A378605 A378606 A378607 * A378610 A378611 A378612

Keyword

nonn,new

Author

John Tyler Rascoe, Dec 01 2024

Status

approved