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

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(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.

Formula

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