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A318395 Number of nonnegative integer matrices with values summing to n, up to transposition and permutation of rows and columns. 1
1, 1, 3, 7, 21, 54, 167, 491, 1586, 5132, 17442, 60399, 216172, 790436, 2965333, 11365813, 44536775, 178107679, 726716229, 3022464373, 12807206008, 55253891494, 242585471236, 1083255591604, 4917631017573, 22685090928596, 106291554085987, 505653658171936, 2441383079595849 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the number of non-isomorphic pairs of set partitions of {1,...,n}.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..50

FORMULA

a(n) = (A007716(n) + A316983(n))/2. - Andrew Howroyd, Sep 03 2018

EXAMPLE

Inequivalent representatives of the a(3) = 7 nonnegative integer matrices:

  [3]   [1 2]   [1 1 1]   [1 0]   [0 1]   [1 0 0]   [1 0 0]

                          [0 2]   [1 1]   [0 1 1]   [0 1 0]

                                                    [0 0 1]

Non-isomorphic representatives of the a(3) = 7 pairs of set partitions:

    {{1,2,3}}     {{1,2,3}}

    {{1,2,3}}    {{1},{2,3}}

    {{1,2,3}}   {{1},{2},{3}}

   {{1},{2,3}}   {{1},{2,3}}

   {{1},{2,3}}   {{2},{1,3}}

   {{1},{2,3}}  {{1},{2},{3}}

  {{1},{2},{3}} {{1},{2},{3}}

CROSSREFS

Cf. A000110, A000258, A001247, A007716, A008277, A049311, A059849, A060639, A116540, A181939, A316983, A318393.

Sequence in context: A098545 A161707 A192068 * A151267 A319558 A307251

Adjacent sequences:  A318392 A318393 A318394 * A318396 A318397 A318398

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 25 2018

EXTENSIONS

a(6)-a(25) from Andrew Howroyd, Sep 03 2018

Terms a(26) and beyond from Andrew Howroyd, Mar 29 2020

STATUS

approved

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Last modified May 26 02:56 EDT 2020. Contains 334613 sequences. (Running on oeis4.)