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

0,3

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

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

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

Adjacent sequences: A331386 A331387 A331388 * A331390 A331391 A331392

Keyword

nonn

Author

Andrew Howroyd, Jan 15 2020

Status

approved