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 A369313 #20 Jan 28 2024 01:45:39
%S A369313 2,4,13,101,3938,3257610,676675164063
%N A369313 Number of interval-closed sets in the boolean lattice of dimension n.
%C A369313 An interval-closed set of a poset is a subset I such that if x and y are in I with x <= z <= y, then z is in I.
%C A369313 Interval-closed sets are also called convex subsets of a poset.
%H A369313 Jennifer Elder, Nadia Lafrenière, Erin McNicholas, Jessica Striker, and Amanda Welch, <a href="http://arxiv.org/abs/2307.08520">Toggling, rowmotion, and homomesy on interval-closed sets</a>, arXiv:2307.08520 [math.CO], 2023.
%e A369313 The a(0) = 2 through a(2) = 13 interval-closed sets:
%e A369313 {} {} {}
%e A369313 {{}} {{}} {{}}
%e A369313 {{1}} {{1}}
%e A369313 {{}{1}} {{2}}
%e A369313 {{12}}
%e A369313 {{}{1}}
%e A369313 {{}{2}}
%e A369313 {{1}{2}}
%e A369313 {{1}{12}}
%e A369313 {{2}{12}}
%e A369313 {{}{1}{2}}
%e A369313 {{1}{2}{12}}
%e A369313 {{}{1}{2}{12}}
%o A369313 (SageMath)
%o A369313 ICS_count = 0
%o A369313 x = Posets.BooleanLattice(n)
%o A369313 for A in x.antichains_iterator():
%o A369313 I = x.order_ideal(A)
%o A369313 Q = x.subposet(set(I).difference(A))
%o A369313 ICS_count += Q.antichains().cardinality()
%o A369313 ICS_count
%Y A369313 Interval-closed sets are a superset of order ideals. Cf. A000372.
%K A369313 nonn,hard,more
%O A369313 0,1
%A A369313 _Nadia Lafreniere_, Jan 19 2024
%E A369313 a(6) from _Christian Sievers_, Jan 27 2024