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A369926
Number of non-isomorphic set multipartitions (multisets of sets) of weight n without endpoints or singletons.
2
1, 0, 0, 0, 1, 0, 3, 1, 9, 8, 34, 45, 177, 324, 1048, 2566, 8050, 22840, 73562, 231978, 780221, 2653042, 9377141, 33820014, 125473936, 475719042, 1846424607, 7317819857, 29611827086, 122190972442, 513900819816, 2201109101784, 9595815668795, 42553843201446, 191861748624324, 879049648551947
OFFSET
0,7
COMMENTS
A singleton is a part of size 1. An endpoint is a vertex that appears in only one part.
a(n) is also the number of binary matrices with a total of n 1's and every row and column sum at least 2 up to permutation of rows and columns.
LINKS
EXAMPLE
The a(8) = 9 matrices are:
[1 1 1 1] [1 1 1] [1 1 1 0] [1 1 1 1]
[1 1 1 1] [1 1 1] [1 1 0 1] [1 1 0 0]
[1 1 0] [0 0 1 1] [0 0 1 1]
.
[1 1] [1 1 0] [1 1 0] [1 1 0 0] [1 1 0 0]
[1 1] [1 1 0] [1 1 0] [1 1 0 0] [1 0 1 0]
[1 1] [1 0 1] [1 0 1] [0 0 1 1] [0 1 0 1]
[1 1] [1 0 1] [0 1 1] [0 0 1 1] [0 0 1 1]
PROG
(PARI) Vec(G(25, 1)) \\ G defined in A369927.
CROSSREFS
Row sums of A369927.
A321677 is the case without singletons but allowing endpoints (or by duality without endpoints but allowing singletons).
Cf. A330055 (set-systems).
Sequence in context: A016601 A193031 A078416 * A223533 A021973 A075498
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Feb 06 2024
STATUS
approved