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A331714
Number of non-isomorphic set-systems with 3 sets each with n elements.
1
1, 5, 12, 25, 44, 73, 112, 166, 235, 325, 436, 575, 742, 945, 1184, 1468, 1797, 2181, 2620, 3125, 3696, 4345, 5072, 5890
OFFSET
1,2
COMMENTS
a(n) is the number of nonequivalent binary matrices with 3 distinct columns and any number of nonzero rows with n ones in every column up to permutation of rows and columns.
EXAMPLE
The a(2) = 5 set systems are:
{{1,2}, {3,4}, {5,6}},
{{1,2}, {1,3}, {4,5}},
{{1,2}, {1,3}, {1,4}},
{{1,2}, {1,3}, {2,4}},
{{1,2}, {1,3}, {2,3}}.
.
These correspond to the following matrices:
[1 0 0] [1 1 0] [1 1 1] [1 1 0] [1 1 0]
[1 0 0] [1 0 0] [1 0 0] [1 0 1] [1 0 1]
[0 1 0] [0 1 0] [0 1 0] [0 1 0] [0 1 1]
[0 1 0] [0 0 1] [0 0 1] [0 0 1]
[0 0 1] [0 0 1]
[0 0 1]
CROSSREFS
Column k=3 of A331508.
Cf. A331713.
Sequence in context: A336877 A212058 A303854 * A086168 A301748 A108201
KEYWORD
nonn,more
AUTHOR
Andrew Howroyd, Jan 31 2020
STATUS
approved