A331653 Number of binary matrices with distinct nonzero rows, a total of n ones and each column with the same number of ones and columns in nonincreasing lexicographic order.

1, 2, 4, 11, 16, 55, 64, 418, 440, 4810, 1024, 99519, 4096, 1711115, 2797136, 43103893, 65536, 1877466431, 262144, 38795757791, 236478538994, 1291635643049, 4194304, 161575200818279, 585914511112, 2019395442729961, 62318195369999169, 119726874231250951, 268435456

Offset: 1

Author

Andrew Howroyd, Jan 24 2020

Keywords

• nonn

Comments

The condition that the columns be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of columns.

Examples

			The a(4) = 11 matrices are:
  [1 0 0 0]  [1 1]  [1 0]  [1 0]  [1 1 0 0]  [1 0 0 0]
  [0 1 0 0]  [1 0]  [1 1]  [0 1]  [0 0 1 0]  [0 1 1 0]
  [0 0 1 0]  [0 1]  [0 1]  [1 1]  [0 0 0 1]  [0 0 0 1]
  [0 0 0 1]
.
  [1 0 0 0]  [1 1 1 0]  [1 1 0 0]  [1 0 0 0]  [1 1 1 1]
  [0 1 0 0]  [0 0 0 1]  [0 0 1 1]  [0 1 1 1]
  [0 0 1 1]
		

Crossrefs

Cf. A331571.

Formula

a(n) = Sum_{d|n} A331571(n/d, d).