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%I #16 Jun 17 2020 16:33:06
%S 1,0,0,3,6,0,0,1646,34040,0,0,16006173014,4525920859198,0,0,
%T 4648429222263945620900,16788801124652327714275292,0,0,
%U 37312554419836846950126367899458469004,1771856721790425759554265832614437952858250,0,0,9390566673339284963209556300602063088163896933170108347086,6044842632698233176498212302295937843763731581533454885103600044
%N Number of simple unlabeled graphs with n nodes and n(n-1)/4 edges.
%H Sebastian Jeon, Tanya Khovanova, <a href="https://arxiv.org/abs/2003.03870">3-Symmetric Graphs</a>, arXiv:2003.03870 [math.CO], 2020.
%e a(1) = 1: There is 1 graph with 1 node and 0 edges.
%e a(2) = 0: There are no graphs with 2 nodes 1/2 edges. (More generally, if n = 2 or 3 mod 4 then a(n) = 0.)
%e a(4) = 3: There are 3 graphs with 4 nodes and 3 edges.
%e a(5) = 6: There are 6 graphs with 5 nodes and 5 edges.
%e a(8) = 1646: There are 1646 graphs with 8 nodes and 28 edges.
%e a(9) = 34040: There are 34040 graphs with 9 nodes and 36 edges.
%t Needs["Combinatorica`"]; Array[If[Mod[#, 4] == 1 || Mod[#, 4] == 0, NumberOfGraphs[#, # (# - 1)/4], 0] &, 25]
%K nonn
%O 1,4
%A _Geoffrey Critzer_, Oct 20 2012
%E Mathematica corrected by _Michael De Vlieger_, Jun 17 2020
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