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A331713
Number of nonnegative integer matrices with pairwise distinct nonzero rows, the total sum of elements equal n, the same sum of elements in each column, and the columns coming in nonincreasing lexicographic order.
2
1, 3, 7, 18, 21, 147, 77, 1119, 2270, 12273, 1089, 464200, 4229, 4148223, 32941976, 159812905, 66153, 10211281004, 263321, 205923976532, 2439257062679, 3086915165084, 4199061, 1526043270802300, 311419986358517, 4817701809545446, 621665561741298232, 1898993198795136209
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} A331572(n/d, d).
EXAMPLE
The a(2) = 3 matrices are:
[1 0] [1 1] [2]
[0 1]
CROSSREFS
Cf. A331572.
Sequence in context: A222452 A218165 A102329 * A348391 A327321 A069143
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 25 2020
STATUS
approved