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A331391
Number of binary matrices with a total of n ones, distinct columns each with the same number of ones and nonzero rows in nonincreasing lexicographic order.
1
1, 2, 2, 4, 2, 14, 2, 76, 31, 801, 2, 12797, 2, 233247, 28480, 5560377, 2, 160866915, 2, 5351339038, 193927186, 208746406130, 2, 9342273087807, 5289613, 470405726166256, 4946464287635, 26636935297440055, 2, 1679266767908385729, 2, 116818412262277969513
OFFSET
1,2
COMMENTS
The condition that the rows be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of rows.
FORMULA
a(n) = Sum{d|n} A331126(n/d, d).
a(p) = 2 for prime p.
EXAMPLE
The a(4) = 4 matrices are:
[1 0 0 0] [1] [1 0] [1 1]
[0 1 0 0] [1] [1 0] [1 0]
[0 0 1 0] [1] [0 1] [0 1]
[0 0 0 1] [1] [0 1]
CROSSREFS
Cf. A331126.
Sequence in context: A126984 A159749 A227293 * A359442 A102416 A333595
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 15 2020
STATUS
approved