

A331509


Array read by antidiagonals: A(n,k) is the number of nonisomorphic T_0 nregular setsystems on a kset.


5



1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 3, 0, 0, 1, 0, 1, 6, 3, 0, 0, 1, 0, 1, 15, 19, 1, 0, 0, 1, 0, 1, 42, 141, 29, 0, 0, 0, 1, 0, 1, 109, 1571, 769, 23, 0, 0, 0, 1, 0, 1, 320
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OFFSET

0,18


COMMENTS

An nregular setsystem is a finite set of nonempty sets in which each element appears in n blocks.
A setsystem is T_0 if for every two distinct elements there exists a block containing one but not the other element.
A(n,k) is the number of nonequivalent binary matrices with k distinct columns and any number of distinct nonzero rows with n ones in every column up to permutation of rows and columns.


LINKS

Table of n, a(n) for n=0..57.


EXAMPLE

Array begins:
=================================
n\k  0 1 2 3 4 5 6 7
+
0  1 1 0 0 0 0 0 0 ...
1  1 1 1 1 1 1 1 1 ...
2  1 0 1 3 6 15 42 109 ...
3  1 0 0 3 19 141 1571 ...
4  1 0 0 1 29 769 ...
5  1 0 0 0 23 ...
...
The A(2,3) = 3 matrices are:
[1 1 1] [1 1 0] [1 1 0]
[1 0 0] [1 0 1] [1 0 1]
[0 1 0] [0 1 0] [0 1 1]
[0 0 1] [0 0 1]


CROSSREFS

Row 2 appears to be A005368.
Cf. A330942, A331039, A331461, A331508, A331510.
Sequence in context: A324874 A324862 A324864 * A171913 A074936 A035655
Adjacent sequences: A331506 A331507 A331508 * A331510 A331511 A331512


KEYWORD

nonn,tabl,more


AUTHOR

Andrew Howroyd, Jan 18 2020


STATUS

approved



