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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..24.

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.

Cf. A032020, A331646, A331712.

Sequence in context: A270357 A108240 A064606 * A223001 A066612 A098637

Adjacent sequences:  A331708 A331709 A331710 * A331712 A331713 A331714

KEYWORD

nonn

AUTHOR

Andrew Howroyd, Jan 25 2020

STATUS

approved

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Last modified October 27 10:47 EDT 2021. Contains 348274 sequences. (Running on oeis4.)