A213434 a(n) is the number of labeled triangle-free simple graphs on n vertices.

1, 2, 7, 41, 388, 5789, 133501, 4682270, 246348115, 19213627145, 2198376297964, 365587270414697, 87628189849380625, 30044424979717359410, 14633141237888767056799, 10059886640779846047089825

Offset: 1

Author

R. H. Hardin, Jun 11 2012

Keywords

• nonn
• more

Comments

Former name: Number of n X n symmetric binary matrices with zero diagonal and no three-node loops x(i,j)*x(j,k)*x(k,i) = 1, i < j < k.

From Brendan McKay, Jun 11 2021: (Start)

EXP transform of A345218.

Labeled version of A006785. (End)

a(n) is the number of sign mappings X:([n] choose 2) -> {+,-} such that for any ordered 3-tuple aManfred Scheucher, Jan 05 2024

Examples

			Some solutions for n=4:
  0 1 0 0     0 1 1 0     0 1 0 0     0 0 1 1     0 1 0 0
  1 0 1 0     1 0 0 1     1 0 0 0     0 0 1 0     1 0 0 1
  0 1 0 1     1 0 0 1     0 0 0 1     1 1 0 0     0 0 0 0
  0 0 1 0     0 1 1 0     0 0 1 0     1 0 0 0     0 1 0 0
		

Links

• Tobias Boege and Thomas Kahle, Construction Methods for Gaussoids, arXiv:1902.11260 [math.CO], 2019.
• Falk Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 8c665c7.

Crossrefs

Cf. A006785, A345218.

Extensions

a(11)-a(13) added using tinygraph by Falk Hüffner, Jun 19 2018

a(14)-a(15) added using tinygraph by Falk Hüffner, Oct 28 2019

a(16) added by Brendan McKay, Sep 15 2020

Name changed to the one suggested by Falk Hüffner and Brendan McKay, Jun 11 2021