A331196 Number of nonnegative integer matrices with n distinct columns and any number of nonzero rows with each column sum being 3 and rows in nonincreasing lexicographic order.

1, 3, 28, 599, 23243, 1440532, 131530132, 16720208200, 2837752812927, 622570020892599, 172077041175850521, 58679982298020226625, 24262822372018694983540, 11986886218243164848742812, 6987708088810202717378639087, 4754544525981425409034078100189

Offset

0,2

Comments

The condition that the rows be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of rows.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A322487(k).

Example

The a(2) = 28 matrices include 6 with 2 rows, 10 with 3 rows, 8 with 4 rows, 3 with 5 rows and 1 with 6 rows. The 16 with 2 or 3 rows are:
   [3 2]  [3 1]  [3 0]  [2 3]  [2 1]  [2 0]  [3 1]  [3 0]
   [0 1]  [0 2]  [0 3]  [1 0]  [1 2]  [1 3]  [0 1]  [0 2]
                                             [0 1]  [0 1]
.
   [2 2]  [2 1]  [2 1]  [2 0]  [2 0]  [2 0]  [1 3]  [1 2]
   [1 0]  [1 1]  [1 0]  [1 2]  [1 1]  [1 0]  [1 0]  [1 1]
   [0 1]  [0 1]  [0 2]  [0 1]  [0 2]  [0 3]  [1 0]  [1 0]

Crossrefs

Row n=3 of A331161.

Cf. A322487.

Sequence in context: A056066 A174483 A092985 * A181588 A084880 A110259

Adjacent sequences: A331193 A331194 A331195 * A331197 A331198 A331199

Keyword

nonn

Author

Andrew Howroyd, Jan 11 2020

Status

approved