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A331509 Array read by antidiagonals: A(n,k) is the number of nonisomorphic T_0 n-regular set-systems on a k-set. 6
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,18
COMMENTS
An n-regular set-system is a finite set of nonempty sets in which each element appears in n blocks.
A set-system 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
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. Row 3 is A331716.
Sequence in context: A324874 A324862 A324864 * A171913 A342154 A074936
KEYWORD
nonn,tabl,more
AUTHOR
Andrew Howroyd, Jan 18 2020
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)