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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
OFFSET
0,3
COMMENTS
Also the number of non-isomorphic pairs of set partitions of {1,...,n}.
LINKS
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}}
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