|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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.
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|