A331655 Number of binary matrices with n distinct columns and any number of distinct nonzero rows with 4 ones in every column and rows in decreasing lexicographic order.

1, 0, 0, 1, 272, 64453, 23553340, 13241130441, 11008118941631, 13027230343637042, 21234181599255320655, 46357847997267210103060, 132373322228662190671151849, 484443861947038578745971380703, 2232754658868099948336222687731941, 12763566506391999019612414249332466653

Offset: 0

Author

Andrew Howroyd, Jan 24 2020

Keywords

• nonn

Comments

The condition that the rows be in decreasing order is equivalent to considering nonequivalent matrices with distinct rows up to permutation of rows.

Examples

			The a(3) = 1 matrix is:
  [1 1 1]
  [1 1 0]
  [1 0 1]
  [1 0 0]
  [0 1 1]
  [0 1 0]
  [0 0 1]
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50

Crossrefs

Row n=4 of A331039.

Cf. A188446.

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A188446(k).