A327235 Number of unlabeled simple graphs with n vertices whose edge-set is not connected.

1, 1, 1, 1, 2, 4, 14, 49, 234, 1476, 15405, 307536, 12651788, 1044977929, 167207997404, 50838593828724, 29156171171238607, 31484900549777534887, 64064043979274771429379, 246064055301339083624989655

Offset

0,5

Links

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

Formula

a(n) = 1 + A000088(n) - Sum_{i = 1..n} A001349(i).

Example

The a(4) = 2 through a(6) = 14 edge-sets:
  {}       {}             {}
  {12,34}  {12,34}        {12,34}
           {12,35,45}     {12,34,56}
           {12,34,35,45}  {12,35,45}
                          {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

Unlabeled non-connected graphs are A000719.

Partial sums of A327075.

The labeled version is A327199.

Cf. A000088, A001349, A002494, A052446, A054592, A327070, A327071.

Sequence in context: A212268 A092665 A046650 * A055727 A003500 A316363

Adjacent sequences: A327232 A327233 A327234 * A327236 A327237 A327238

Keyword

nonn

Author

Gus Wiseman, Sep 01 2019

Status

approved