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A316983
Number of non-isomorphic self-dual multiset partitions of weight n.
103
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
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
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]
PROG
(PARI) vector(25, n, n--; T(n, n)) \\ T(n, k) defined in A318805. - Andrew Howroyd, Jan 16 2024
CROSSREFS
Row sums of A320796.
Main diagonal of A318805.
Sequence in context: A245122 A291728 A268649 * A136326 A362033 A059973
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 18 2018
EXTENSIONS
Terms a(9) and beyond from Andrew Howroyd, Sep 03 2018
STATUS
approved