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A331711
Number of nonnegative integer matrices with 2 columns and any number of distinct nonzero rows with column sums n and columns in nonincreasing lexicographic order.
3
1, 2, 7, 45, 271, 1244, 7289, 40841, 201103, 1044720, 5172055, 24532739, 116470697, 546142112, 2505755203, 11318525367, 50046273319, 219637249886, 944072864849, 4029243438335, 16977344151163, 70370874105726, 289702060533067, 1177283903981765, 4740700176816041
OFFSET
0,2
COMMENTS
The condition that the columns be in nonincreasing order is equivalent to considering nonequivalent matrices up to permutation of columns.
FORMULA
a(n) = (A331646(n) + A032020(n)) / 2.
EXAMPLE
The a(2) = 2 matrices are:
[1 1] [1 0] [1 0] [2 1] [2 0] [1 0] [2 2]
[1 0] [1 1] [0 1] [0 1] [0 2] [1 2]
[0 1] [0 1] [1 1]
CROSSREFS
Column k=2 of A331572.
Sequence in context: A367787 A108240 A064606 * A223001 A066612 A098637
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 25 2020
STATUS
approved