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A330053
Number of non-isomorphic set-systems of weight n with at least one singleton.
6
0, 1, 1, 3, 6, 14, 32, 79, 193, 499, 1321, 3626, 10275, 30126, 91062, 284093, 912866, 3018825, 10261530, 35814255, 128197595, 470146011, 1764737593, 6773539331, 26561971320, 106330997834, 434195908353, 1807306022645, 7663255717310, 33079998762373
OFFSET
0,4
COMMENTS
A set-system is a finite set of finite nonempty sets of positive integers. An singleton is an edge of size 1. The weight of a set-system is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
LINKS
Jean-François Alcover, Table of n, a(n) for n = 0..50 [using data from A283877 and A306005]
FORMULA
a(n) = A283877(n) - A306005(n). - Jean-François Alcover, Feb 09 2020
EXAMPLE
Non-isomorphic representatives of the a(1) = 1 through a(5) = 14 multiset partitions:
{1} {1}{2} {1}{12} {1}{123} {1}{1234}
{1}{23} {1}{234} {1}{2345}
{1}{2}{3} {1}{2}{12} {1}{12}{13}
{1}{2}{13} {1}{12}{23}
{1}{2}{34} {1}{12}{34}
{1}{2}{3}{4} {1}{2}{123}
{1}{2}{134}
{1}{2}{345}
{1}{23}{45}
{2}{13}{14}
{1}{2}{3}{12}
{1}{2}{3}{14}
{1}{2}{3}{45}
{1}{2}{3}{4}{5}
MATHEMATICA
A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
A283877 = A@283877;
A306005 = A@306005;
a[n_] := A283877[[n + 1]] - A306005[[n + 1]];
a /@ Range[0, 50] (* Jean-François Alcover, Feb 09 2020 *)
CROSSREFS
The complement is counted by A306005.
The multiset partition version is A330058.
Non-isomorphic set-systems with at least one endpoint are A330052.
Non-isomorphic set-systems counted by vertices are A000612.
Non-isomorphic set-systems counted by weight are A283877.
Sequence in context: A272362 A182905 A373456 * A192678 A114945 A003477
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 30 2019
STATUS
approved