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

Author

Andrew Howroyd, Jan 11 2020

Keywords

• nonn

Comments

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

Examples

			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]
		

Links

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

Crossrefs

Row n=3 of A331161.

Cf. A322487.

Formula

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