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A057151
Number of square binary matrices with n ones, with no zero rows or columns, up to row and column permutation.
15
1, 1, 2, 4, 8, 18, 41, 102, 252, 666, 1789, 5031, 14486, 43280, 132777, 420267, 1366307, 4566966, 15661086, 55081118, 198425478, 731661754, 2758808581, 10629386376, 41814350148, 167830018952, 686822393793, 2864024856054, 12162059027416, 52564545391789
OFFSET
1,3
COMMENTS
Number of square binary matrices with n ones and with no zero rows or columns is A104602(n). - Vladeta Jovovic, Mar 25 2006
Also the number of non-isomorphic square set multipartitions (multisets of sets) of weight n. A multiset partition or hypergraph is square if its length (number of blocks or edges) is equal to its number of vertices. The weight of a multiset partition is the sum of sizes of its parts. - Gus Wiseman, Nov 16 2018
LINKS
EXAMPLE
There are 666 square binary matrices with 10 ones, with no zero rows or columns, up to row and column permutation: 33 of size 4 X 4, 248 of size 5 X 5, 288 of size 6 X 6, 79 of size 7 X 7, 15 of size 8 X 8, 2 of size 9 X 9 and 1 of size 10 X 10. Cf. A057150.
From Gus Wiseman, Nov 16 2018: (Start)
Non-isomorphic representatives of the a(1) = 1 through a(6) = 18 square set multipartitions:
{1} {1}{2} {2}{12} {12}{12} {1}{23}{23} {12}{13}{23}
{1}{2}{3} {1}{1}{23} {2}{13}{23} {1}{23}{123}
{1}{3}{23} {2}{3}{123} {13}{23}{23}
{1}{2}{3}{4} {3}{13}{23} {3}{23}{123}
{3}{3}{123} {1}{1}{1}{234}
{1}{2}{2}{34} {1}{1}{24}{34}
{1}{2}{4}{34} {1}{1}{4}{234}
{1}{2}{3}{4}{5} {1}{2}{34}{34}
{1}{3}{24}{34}
{1}{3}{4}{234}
{1}{4}{24}{34}
{1}{4}{4}{234}
{2}{4}{12}{34}
{3}{4}{12}{34}
{4}{4}{12}{34}
{1}{2}{3}{3}{45}
{1}{2}{3}{5}{45}
{1}{2}{3}{4}{5}{6}
(End)
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Aug 14 2000
EXTENSIONS
More terms from Max Alekseyev, May 31 2007
STATUS
approved