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A218113
Number of simple unlabeled graphs with n nodes and n(n-1)/4 edges.
0
1, 0, 0, 3, 6, 0, 0, 1646, 34040, 0, 0, 16006173014, 4525920859198, 0, 0, 4648429222263945620900, 16788801124652327714275292, 0, 0, 37312554419836846950126367899458469004, 1771856721790425759554265832614437952858250, 0, 0, 9390566673339284963209556300602063088163896933170108347086, 6044842632698233176498212302295937843763731581533454885103600044
OFFSET
1,4
LINKS
Sebastian Jeon, Tanya Khovanova, 3-Symmetric Graphs, arXiv:2003.03870 [math.CO], 2020.
EXAMPLE
a(1) = 1: There is 1 graph with 1 node and 0 edges.
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.)
a(4) = 3: There are 3 graphs with 4 nodes and 3 edges.
a(5) = 6: There are 6 graphs with 5 nodes and 5 edges.
a(8) = 1646: There are 1646 graphs with 8 nodes and 28 edges.
a(9) = 34040: There are 34040 graphs with 9 nodes and 36 edges.
MATHEMATICA
Needs["Combinatorica`"]; Array[If[Mod[#, 4] == 1 || Mod[#, 4] == 0, NumberOfGraphs[#, # (# - 1)/4], 0] &, 25]
CROSSREFS
Sequence in context: A371334 A154924 A071105 * A295194 A104613 A113565
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Oct 20 2012
EXTENSIONS
Mathematica corrected by Michael De Vlieger, Jun 17 2020
STATUS
approved