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A108800 Number of nonisomorphic systems enumerated by A102895. 15

%I

%S 1,2,6,28,330,28960,216562364,5592326182940100

%N Number of nonisomorphic systems enumerated by A102895.

%C Also the number of non-isomorphic sets of sets with {} that are closed under intersection. Also the number of non-isomorphic set-systems (without {}) covering n + 1 vertices and closed under intersection. - _Gus Wiseman_, Aug 05 2019

%H M. Habib and L. Nourine, <a href="https://doi.org/10.1016/j.disc.2004.11.010">The number of Moore families on n = 6</a>, Discrete Math., 294 (2005), 291-296.

%F a(n > 0) = 2 * A108798(n).

%e From _Gus Wiseman_, Aug 02 2019: (Start)

%e Non-isomorphic representatives of the a(0) = 1 through a(3) = 28 sets of sets with {} that are closed under intersection:

%e {} {} {} {}

%e {}{1} {}{1} {}{1}

%e {}{12} {}{12}

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

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

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

%e {}{2}{12}

%e {}{3}{123}

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

%e {}{23}{123}

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

%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}

%e (End)

%Y Except a(0) = 1, first differences of A193675.

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

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

%Y The labeled version is A102895.

%Y The case also closed under union is A326898.

%Y The covering case is A326883.

%Y Cf. A001930, A102894, A102896, A102897, A193674, A326880, A326881.

%K nonn,more

%O 0,2

%A _Don Knuth_, Jul 01 2005

%E a(6) added (using A193675) by _N. J. A. Sloane_, Aug 02 2011

%E Changed a(0) from 2 to 1 by _Gus Wiseman_, Aug 02 2019

%E a(7) added (using A108798) by _Andrew Howroyd_, Aug 10 2019

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Last modified January 28 03:42 EST 2020. Contains 331317 sequences. (Running on oeis4.)