A218113 Number of simple unlabeled graphs with n nodes and n(n-1)/4 edges.

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

Table of n, a(n) for n=1..25.

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

Adjacent sequences: A218110 A218111 A218112 * A218114 A218115 A218116

Keyword

nonn

Author

Geoffrey Critzer, Oct 20 2012

Extensions

Mathematica corrected by Michael De Vlieger, Jun 17 2020

Status

approved