login
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, 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.
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 24 2020
STATUS
approved