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

1,2

Comments

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

Links

Table of n, a(n) for n=1..29.

Formula

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

Example

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.

Sequence in context: A277867 A278595 A005822 * A286293 A167801 A216554

Adjacent sequences: A331650 A331651 A331652 * A331654 A331655 A331656

Keyword

nonn

Author

Andrew Howroyd, Jan 24 2020

Status

approved