OFFSET
1,3
LINKS
Simon Dreyer, Antoine Genitrini, and Mehdi Naima, Asymptotic Enumeration of Labeled Triangle-Free Graphs through the Combinatorics of Directed Acyclic Graphs of Shortest Paths, hal:05609965, 2026.
Vaclav Kotesovec, Plot of a(n) / (2^(n^2/4+n-1/2)/sqrt(Pi*n)) for n = 1..16
Vaclav Kotesovec, Plot of A001832(n) / a(n) for n = 1..16
Kai Wang, An Efficient Algorithm to Generate all Labeled Triangle-free Graphs with a given Graphical Degree Sequence, arXiv:2601.15943 [math.CO], 2026. See p. 5.
FORMULA
a(n) ~ c * 2^(n^2/4+n-1/2)/sqrt(Pi*n), where c = Sum_{k = -oo..oo} 2^(-k^2) = EllipticTheta[3, 0, 1/2] = 2.128936827211877... if n is even and c = Sum_{k = -oo..oo} 2^(-(k+1/2)^2) = EllipticTheta[2, 0, 1/2] = 2.12893125051302... if n is odd. See A213434 for additional comments. - Mehdi Naima, Jun 08 2026
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Brendan McKay, Jun 11 2021
STATUS
approved