This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382829 #5 Apr 12 2025 12:00:06 %S A382829 1,1,2,5,15,51,197,864,4325,24922 %N A382829 Number of distinct rank vectors of distributive lattices of height n. %C A382829 Distributive lattices are ranked posets, and we define the rank vector of a ranked poset P as the vector whose k-th coordinate (starting at k = 0) is the number of elements of rank k in P. %C A382829 By Birkhoff's representation theorem, elements of a finite distributive lattice L are in bijection with lower sets of the poset of join-irreducible elements of L, an element of rank k corresponding to a lower of set size k. %e A382829 The rank vectors corresponding to a(4) = 15 are: %e A382829 (1, 1, 1, 1, 1), (1, 1, 1, 2, 1), (1, 1, 2, 1, 1), %e A382829 (1, 1, 2, 2, 1), (1, 1, 3, 3, 1), (1, 2, 1, 1, 1), %e A382829 (1, 2, 1, 2, 1), (1, 2, 2, 1, 1), (1, 2, 2, 2, 1), %e A382829 (1, 2, 3, 2, 1), (1, 2, 3, 3, 1), (1, 3, 3, 1, 1), %e A382829 (1, 3, 3, 2, 1), (1, 3, 4, 3, 1), (1, 4, 6, 4, 1). %e A382829 Two non-isomorphic distributive lattices have for rank vector (1, 2, 2, 2, 1). %Y A382829 Cf. A000112, A006982. %K A382829 nonn,more %O A382829 0,3 %A A382829 _Ludovic Schwob_, Apr 06 2025