A316974 Number of non-isomorphic strict multiset partitions of {1, 1, 2, 2, 3, 3, ..., n, n}.

1, 1, 4, 14, 49, 173, 652, 2494

Offset

0,3

Comments

Also the number of unlabeled multigraphs with n edges, allowing loops, spanning an initial interval of positive integers with no equivalent vertices (two vertices are equivalent if in every edge the multiplicity of the first is equal to the multiplicity of the second). For example, non-isomorphic representatives of the a(2) = 4 multigraphs are {(1,2),(1,3)}, {(1,1),(1,2)}, {(1,1),(2,2)}, {(1,1),(1,1)}.

Links

Table of n, a(n) for n=0..7.

Example

Non-isomorphic representatives of the a(3) = 14 strict multiset partitions:
  (112233),
  (1)(12233), (11)(2233), (12)(1233), (112)(233),
  (1)(2)(1233), (1)(12)(233), (1)(23)(123), (2)(11)(233), (11)(22)(33), (12)(13)(23),
  (1)(2)(3)(123), (1)(2)(12)(33), (1)(2)(13)(23).

Crossrefs

Cf. A001055, A007716, A007717, A007719, A020554, A020555, A045778, A050535, A053419, A061742, A094574, A162247, A316892, A316972.

Sequence in context: A071737 A071741 A211305 * A278026 A001894 A215493

Adjacent sequences: A316971 A316972 A316973 * A316975 A316976 A316977

Keyword

nonn,more

Author

Gus Wiseman, Jul 17 2018

Extensions

a(7) from Andrew Howroyd, Feb 07 2020

Status

approved