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A331389
Number of binary matrices with n distinct columns and any number of nonzero rows with 3 ones in every column and rows in nonincreasing lexicographic order.
2
1, 1, 3, 29, 666, 28344, 1935054, 193926796, 26892165502, 4946464286746, 1168900475263013, 346080409272270888, 125798338606148948325, 55204084562033205121607, 28834556615453989801860765, 17710828268156331289770544579, 12658784968736373972502731143309
OFFSET
0,3
COMMENTS
The condition that the rows be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of rows.
a(n) is the number of T_0 3-regular set multipartitions (multisets of sets) on an n-set.
LINKS
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n,k)*A165434(k). - Andrew Howroyd, Jan 31 2020
EXAMPLE
The a(2) = 3 matrices are:
[1 0] [1 1] [1 1]
[1 0] [1 0] [1 1]
[1 0] [1 0] [1 0]
[0 1] [0 1] [0 1]
[0 1] [0 1]
[0 1]
CROSSREFS
Row n=3 of A331126.
Cf. A165434.
Sequence in context: A092251 A304553 A326337 * A243435 A064570 A117264
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 15 2020
STATUS
approved