A326883 - OEIS

%I #9 Aug 11 2019 12:23:55

%S 1,1,4,22,302,28630,216533404,5592325966377736

%N Number of unlabeled set-systems with {} that are closed under intersection and cover n vertices.

%F a(n) = A108800(n) - A108800(n-1) for n > 0. - _Andrew Howroyd_, Aug 10 2019

%e Non-isomorphic representatives of the a(0) = 1 through a(3) = 22 set-systems:

%e   {{}}  {{}{1}}  {{}{12}}        {{}{123}}

%e                  {{}{1}{2}}      {{}{1}{23}}

%e                  {{}{2}{12}}     {{}{3}{123}}

%e                  {{}{1}{2}{12}}  {{}{1}{2}{3}}

%e                                  {{}{23}{123}}

%e                                  {{}{1}{3}{23}}

%e                                  {{}{2}{3}{123}}

%e                                  {{}{3}{13}{23}}

%e                                  {{}{1}{23}{123}}

%e                                  {{}{3}{23}{123}}

%e                                  {{}{1}{2}{3}{23}}

%e                                  {{}{1}{2}{3}{123}}

%e                                  {{}{2}{3}{13}{23}}

%e                                  {{}{1}{3}{23}{123}}

%e                                  {{}{2}{3}{23}{123}}

%e                                  {{}{3}{13}{23}{123}}

%e                                  {{}{1}{2}{3}{13}{23}}

%e                                  {{}{1}{2}{3}{23}{123}}

%e                                  {{}{2}{3}{13}{23}{123}}

%e                                  {{}{1}{2}{3}{12}{13}{23}}

%e                                  {{}{1}{2}{3}{13}{23}{123}}

%e                                  {{}{1}{2}{3}{12}{13}{23}{123}}

%Y The case also closed under union is A001930.

%Y The connected case (i.e., with maximum) is A108798.

%Y The same for union instead of intersection is (also) A108798.

%Y The non-covering case is A108800.

%Y The labeled case is A326881.

%Y Cf. A000798, A102894, A102895, A102897, A193674, A193675, A306445, A326875, A326878, A326880.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Jul 30 2019

%E a(5)-a(7) from _Andrew Howroyd_, Aug 10 2019