

A330231


Number of distinct setsystems that can be obtained by permuting the vertices of the setsystem with BIInumber n.


13



1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 6, 6, 3, 1, 2, 3, 6, 3, 3, 6, 6, 2, 1, 6, 3, 6, 6, 3, 3, 1, 3, 2, 6, 3, 6, 3, 6, 2, 6, 1, 3, 6, 3, 6, 3, 3, 6, 6, 3, 1, 3, 3, 3, 3, 6, 6, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 6, 6, 3, 3, 3, 3, 1, 3, 6, 6, 3, 3, 6, 3, 6, 3, 3, 6
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OFFSET

0,6


COMMENTS

A setsystem is a finite set of finite nonempty sets.
A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793. We define the setsystem with BIInumber n to be obtained by taking the binary indices of each binary index of n. Every setsystem has a different BIInumber. For example, 18 has reversed binary expansion (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BIInumber of {{2},{1,3}} is 18. Elements of a setsystem are sometimes called edges.


LINKS

Table of n, a(n) for n=0..86.


FORMULA

a(n) is a divisor of A326702(n)!.


EXAMPLE

30 is the MMnumber of {{2},{3},{1,2},{1,3}}, with vertex permutations
{{1},{2},{1,3},{2,3}}
{{1},{3},{1,2},{2,3}}
{{2},{3},{1,2},{1,3}}
so a(30) = 3.


MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]], i}, {i, Length[p]}])], {p, Permutations[Union@@m]}]];
Table[Length[graprms[bpe/@bpe[n]]], {n, 0, 100}]


CROSSREFS

Positions of 1's are A330217.
Positions of first appearances are A330218.
The version for MMnumbers is A330098.
Achiral setsystems are counted by A083323.
BIInumbers of fully chiral setsystems are A330226.
Cf. A000120, A003238, A007716, A016031, A048793, A055621, A070939, A214577, A326031, A326702, A330101, A330195, A330229, A330230, A330233.
Sequence in context: A227736 A228528 A219244 * A323017 A273638 A277582
Adjacent sequences: A330228 A330229 A330230 * A330232 A330233 A330234


KEYWORD

nonn


AUTHOR

Gus Wiseman, Dec 09 2019


STATUS

approved



