A331654 Number of binary matrices with a total of n ones, distinct columns each with the same number of ones and distinct nonzero rows in decreasing lexicographic order.

1, 1, 1, 2, 1, 6, 1, 44, 6, 519, 1, 8363, 1, 163357, 9427, 3988615, 1, 117148318, 1, 3986012464, 84012192, 157783127674, 1, 7143740399835, 248686, 364166073164915, 2479642897110, 20827974319925302, 1, 1324585467847848929, 1, 92917902002561639120, 190678639438170503

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = Sum_{d|n} A331039(n/d, d).

Example

The a(6) = 6 matrices are:
  [1 0 0 0 0 0]  [1 1 1]  [1 1 0]  [1 1 0]  [1 0 1]  [1 1 0]
  [0 1 0 0 0 0]  [1 0 0]  [1 0 1]  [1 0 0]  [1 0 0]  [1 0 1]
  [0 0 1 0 0 0]  [0 1 0]  [0 1 0]  [0 1 1]  [0 1 1]  [0 1 1]
  [0 0 0 1 0 0]  [0 0 1]  [0 0 1]  [0 0 1]  [0 1 0]
  [0 0 0 0 1 0]
  [0 0 0 0 0 1]

Crossrefs

Cf. A331039.

Sequence in context: A083720 A369925 A055878 * A346864 A302690 A030304

Adjacent sequences: A331651 A331652 A331653 * A331655 A331656 A331657

Keyword

nonn

Author

Andrew Howroyd, Jan 24 2020

Status

approved