A327075 Number of non-connected unlabeled simple graphs covering n vertices.

1, 0, 0, 0, 1, 2, 10, 35, 185, 1242, 13929, 292131, 12344252, 1032326141, 166163019475, 50671385831320, 29105332577409883, 31455744378606296280, 64032559078724993894492, 245999991257359808853560276

Offset

0,6

Comments

We consider the empty graph to be neither connected (one component) nor disconnected (more than one component).

Links

Table of n, a(n) for n=0..19.

Gus Wiseman, The a(4) = 1 through a(6) = 10 non-connected covering graphs.

Formula

a(n) = A002494(n) - A001349(n), if we assume A001349(0) = A001349(1) = 0.

Example

Non-isomorphic representatives of the a(0) = 1 through a(6) = 10 graphs (empty columns not shown):
  {}  {12,34}  {12,35,45}     {12,34,56}
               {12,34,35,45}  {12,35,46,56}
                              {12,36,46,56}
                              {13,23,46,56}
                              {12,34,35,46,56}
                              {12,36,45,46,56}
                              {13,23,45,46,56}
                              {12,13,23,45,46,56}
                              {12,35,36,45,46,56}
                              {12,34,35,36,45,46,56}

Crossrefs

Column k = 0 of A327201.

The labeled version is A327070.

Disconnected graphs are A000719.

Cf. A000088, A001187, A001349, A002494, A006129, A054592.

Sequence in context: A100230 A220255 A146983 * A135963 A140954 A309889

Adjacent sequences: A327072 A327073 A327074 * A327076 A327077 A327078

Keyword

nonn

Author

Gus Wiseman, Aug 26 2019

Status

approved