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 A316983 Number of non-isomorphic self-dual multiset partitions of weight n. 93
 1, 1, 2, 4, 9, 17, 36, 72, 155, 319, 677, 1429, 3094, 6648, 14518, 31796, 70491, 156818, 352371, 795952, 1813580, 4155367, 9594425, 22283566, 52122379, 122631874, 290432439, 691831161, 1658270316, 3997272089, 9692519896, 23631827354, 57943821449, 142834652193 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of nonnegative integer square symmetric matrices with sum of elements equal to n, under row and column permutations. The dual of a multiset partition has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex, counted with multiplicity. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 EXAMPLE Non-isomorphic representatives of the a(4) = 9 self-dual multiset partitions:   (1111),   (1)(222), (2)(122), (11)(22), (12)(12),   (1)(1)(23), (1)(2)(33), (1)(3)(23),   (1)(2)(3)(4). The a(4) = 9 square symmetric matrices: . [4] . . [3 0]  [2 0]  [2 1]  [1 1] . [0 1]  [0 2]  [1 0]  [1 1] . . [2 0 0]  [1 1 0]  [0 1 1] . [0 1 0]  [1 0 0]  [1 0 0] . [0 0 1]  [0 0 1]  [1 0 0] . . [1 0 0 0] . [0 1 0 0] . [0 0 1 0] . [0 0 0 1] CROSSREFS Main diagonal of A318805. Cf. A000009, A001055, A007716, A007717, A020555, A045778. Cf. A316974, A316978, A316979, A316980, A316981. Sequence in context: A245122 A291728 A268649 * A136326 A059973 A030035 Adjacent sequences:  A316980 A316981 A316982 * A316984 A316985 A316986 KEYWORD nonn AUTHOR Gus Wiseman, Jul 18 2018 EXTENSIONS Terms a(9) and beyond from Andrew Howroyd, Sep 03 2018 STATUS approved

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Last modified June 21 08:18 EDT 2021. Contains 345358 sequences. (Running on oeis4.)