A003190 Number of connected 2-plexes.

1, 0, 1, 3, 29, 2101, 7011181, 1788775603301, 53304526022885278403, 366299663378889804782330207902, 1171638318502622784366970315262493034215728, 3517726593606524901243694560022510194169866584119717555335

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

The Palmer reference (incorrectly) has a(7)=7011349, a(8)=1788775603133, a(9)=53304526022885278659. - Sean A. Irvine, Mar 05 2015

Also connected 3-uniform hypergraphs on n vertices. - Gus Wiseman, Feb 23 2019

Examples

			From _Gus Wiseman_, Feb 23 2019: (Start)
Non-isomorphic representatives of the a(5) = 29 2-plexes:
  {{125}{345}}
  {{123}{245}{345}}
  {{135}{245}{345}}
  {{145}{245}{345}}
  {{123}{145}{245}{345}}
  {{124}{135}{245}{345}}
  {{125}{135}{245}{345}}
  {{134}{235}{245}{345}}
  {{145}{235}{245}{345}}
  {{123}{124}{135}{245}{345}}
  {{123}{145}{235}{245}{345}}
  {{124}{134}{235}{245}{345}}
  {{134}{145}{235}{245}{345}}
  {{135}{145}{235}{245}{345}}
  {{145}{234}{235}{245}{345}}
  {{123}{124}{134}{235}{245}{345}}
  {{123}{134}{145}{235}{245}{345}}
  {{123}{145}{234}{235}{245}{345}}
  {{124}{135}{145}{235}{245}{345}}
  {{125}{135}{145}{235}{245}{345}}
  {{135}{145}{234}{235}{245}{345}}
  {{123}{124}{135}{145}{235}{245}{345}}
  {{124}{135}{145}{234}{235}{245}{345}}
  {{125}{135}{145}{234}{235}{245}{345}}
  {{134}{135}{145}{234}{235}{245}{345}}
  {{123}{124}{135}{145}{234}{235}{245}{345}}
  {{125}{134}{135}{145}{234}{235}{245}{345}}
  {{124}{125}{134}{135}{145}{234}{235}{245}{345}}
  {{123}{124}{125}{134}{135}{145}{234}{235}{245}{345}}
(End)
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
• E. M. Palmer, On the number of n-plexes, Discrete Math., 6 (1973), 377-390.

Crossrefs

Column k=3 of A301924.

Cf. A000665 (unlabeled 3-uniform), A025035, A125791 (labeled 3-uniform), A289837, A301922, A302374 (labeled 3-uniform spanning), A302394, A306017, A319540, A320395, A322451 (unlabeled 3-uniform spanning), A323292-A323299.

Formula

Inverse Euler transform of A000665. - Sean A. Irvine, Mar 05 2015

Extensions

a(7)-a(9) corrected and extended by Sean A. Irvine, Mar 05 2015