cp's OEIS Frontend

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

%I A213434 #43 Jan 06 2024 12:06:02
%S A213434 1,2,7,41,388,5789,133501,4682270,246348115,19213627145,2198376297964,
%T A213434 365587270414697,87628189849380625,30044424979717359410,
%U A213434 14633141237888767056799,10059886640779846047089825
%N A213434 a(n) is the number of labeled triangle-free simple graphs on n vertices.
%C A213434 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.
%C A213434 From _Brendan McKay_, Jun 11 2021: (Start)
%C A213434 EXP transform of A345218.
%C A213434 Labeled version of A006785. (End)
%C A213434 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
%H A213434 Tobias Boege and Thomas Kahle, <a href="https://arxiv.org/abs/1902.11260">Construction Methods for Gaussoids</a>, arXiv:1902.11260 [math.CO], 2019.
%H A213434 Falk Hüffner, <a href="https://github.com/falk-hueffner/tinygraph">tinygraph</a>, software for generating integer sequences based on graph properties, version 8c665c7.
%e A213434 Some solutions for n=4:
%e A213434   0 1 0 0     0 1 1 0     0 1 0 0     0 0 1 1     0 1 0 0
%e A213434   1 0 1 0     1 0 0 1     1 0 0 0     0 0 1 0     1 0 0 1
%e A213434   0 1 0 1     1 0 0 1     0 0 0 1     1 1 0 0     0 0 0 0
%e A213434   0 0 1 0     0 1 1 0     0 0 1 0     1 0 0 0     0 1 0 0
%Y A213434 Cf. A006785, A345218.
%K A213434 nonn,more
%O A213434 1,2
%A A213434 _R. H. Hardin_, Jun 11 2012
%E A213434 a(11)-a(13) added using tinygraph by _Falk Hüffner_, Jun 19 2018
%E A213434 a(14)-a(15) added using tinygraph by _Falk Hüffner_, Oct 28 2019
%E A213434 a(16) added by _Brendan McKay_, Sep 15 2020
%E A213434 Name changed to the one suggested by _Falk Hüffner_ and _Brendan McKay_, Jun 11 2021