|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|