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