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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
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 (list; graph; refs; listen; history; text; internal format)
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
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]
CROSSREFS
Cf. A331570.
Sequence in context: A159585 A130334 A320537 * A227289 A200742 A178729
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 25 2020
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)