OFFSET
0,4
COMMENTS
The unlabeled version is A372169.
LINKS
Eric Weisstein's World of Mathematics, Triangle-Free Graph
FORMULA
Binomial transform is A213434.
EXAMPLE
The a(4) = 22 graphs are:
12-34
13-24
14-23
12-13-14
12-13-24
12-13-34
12-14-23
12-14-34
12-23-24
12-23-34
12-24-34
13-14-23
13-14-24
13-23-24
13-23-34
13-24-34
14-23-24
14-23-34
14-24-34
12-13-24-34
12-14-23-34
13-14-23-24
MATHEMATICA
cys[y_]:=Select[Subsets[Union@@y, {3}], MemberQ[y, {#[[1]], #[[2]]}] && MemberQ[y, {#[[1]], #[[3]]}] && MemberQ[y, {#[[2]], #[[3]]}]&];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&Length[cys[#]]==0&]], {n, 0, 5}]
CROSSREFS
The unlabeled version is A372169.
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Apr 23 2024
STATUS
approved