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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.
3
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
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
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 11 2020
STATUS
approved