A331708 - OEIS

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A331708

Number of nonnegative integer matrices with distinct nonzero rows, total sum n, distinct columns with equals sums and columns in decreasing lexicographic order.

1, 2, 4, 10, 6, 100, 14, 832, 1928, 9280, 66, 409928, 134, 3138847, 32173339, 134531629, 618, 9353244335, 1178, 183394485615, 2395983801112, 2311773448717, 4758, 1479147860804022, 311353753955807, 3599356750729620, 613047176698674761, 1842753685676233794, 30462

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OFFSET

1,2

COMMENTS

The condition that the columns be in decreasing order is equivalent to considering nonequivalent matrices with distinct columns up to permutation of columns.

LINKS

Table of n, a(n) for n=1..29.

FORMULA

a(n) = Sum_{d|n} A331570(n/d, d).

EXAMPLE

The a(4) = 10 matrices are:

[1 0 0 0] [1 1] [1 0] [1 0]

[0 1 0 0] [1 0] [1 1] [0 1]

[0 0 1 0] [0 1] [0 1] [1 1]

[0 0 0 1]

[2 1] [2 0] [1 0] [3] [1] [4]

[0 1] [0 2] [1 2] [1] [3]