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A330158
Number of nonnegative integer matrices with total sum n, distinct columns with equal sums and any number of nonzero rows in nonincreasing lexicographic order.
2
1, 3, 4, 13, 8, 83, 16, 530, 630, 5620, 57, 119889, 102, 1901749, 1498322, 50091143, 298, 1649302673, 491, 54919254373, 16723808377, 2269075359300, 1256, 110133775311277, 26852941986, 5707320920415984, 622570195638208, 339574840900645411, 4566, 22572315004012650868
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} A331161(n/d, d).
EXAMPLE
The a(4) = 13 matrices are:
[1 0 0 0] [1 0] [1] [1 1] [2 0] [1 0] [2]
[0 1 0 0] [1 0] [1] [1 0] [0 1] [1 0] [1]
[0 0 1 0] [0 1] [1] [0 1] [0 1] [0 2] [1]
[0 0 0 1] [0 1] [1]
.
[2 1] [2 0] [1 2] [3] [2] [4]
[0 1] [0 2] [1 0] [1] [2]
CROSSREFS
Cf. A331161.
Sequence in context: A324501 A359112 A342675 * A082197 A138101 A287089
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 11 2020
STATUS
approved