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.

1, 1, 3, 29, 666, 28344, 1935054, 193926796, 26892165502, 4946464286746, 1168900475263013, 346080409272270888, 125798338606148948325, 55204084562033205121607, 28834556615453989801860765, 17710828268156331289770544579, 12658784968736373972502731143309

Offset: 0

Author

Andrew Howroyd, Jan 15 2020

Keywords

• nonn

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.

Examples

			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]
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100

Crossrefs

Row n=3 of A331126.

Cf. A165434.

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A165434(k). - Andrew Howroyd, Jan 31 2020