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

1,2

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 a<b<c we have X(ab)X(ac)X(bc) not equal to +++. - Manfred Scheucher, Jan 05 2024

Links

Table of n, a(n) for n=1..16.

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.

Example

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

Crossrefs

Cf. A006785, A345218.

Sequence in context: A047864 A173916 A163921 * A331920 A008934 A084871

Adjacent sequences: A213431 A213432 A213433 * A213435 A213436 A213437

Keyword

nonn,more

Author

R. H. Hardin, Jun 11 2012

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

Status

approved