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

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]

Crossrefs

Cf. A331570.

Sequence in context: A130334 A375597 A320537 * A227289 A200742 A178729

Adjacent sequences: A331705 A331706 A331707 * A331709 A331710 A331711

Keyword

nonn

Author

Andrew Howroyd, Jan 25 2020

Status

approved