OFFSET
0,5
COMMENTS
An undirected cycle in a graph is a sequence of distinct vertices, up to rotation and reversal, such that there are edges between all consecutive elements, including the last and the first.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: B(x)*C(x) where B(x) is the e.g.f. of A057500 and C(x) is the e.g.f. of A001858. - Andrew Howroyd, Jul 31 2024
EXAMPLE
The a(4) = 19 graphs:
12,13,23
12,14,24
13,14,34
23,24,34
12,13,14,23
12,13,14,24
12,13,14,34
12,13,23,24
12,13,23,34
12,13,24,34
12,14,23,24
12,14,23,34
12,14,24,34
12,23,24,34
13,14,23,24
13,14,23,34
13,14,24,34
13,23,24,34
14,23,24,34
MATHEMATICA
cyc[y_]:=Select[Join@@Table[Select[Join@@Permutations /@ Subsets[Union@@y, {k}], And @@ Table[MemberQ[Sort/@y, Sort[{#[[i]], #[[If[i==k, 1, i+1]]]}]], {i, k}]&], {k, 3, Length[y]}], Min@@#==First[#]&];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Length[cyc[#]]==2&]], {n, 0, 5}]
PROG
(PARI) seq(n)={my(w=lambertw(-x+O(x*x^n))); Vec(serlaplace(exp(-w-w^2/2)*(-log(1+w)/2 + w/2 - w^2/4)), -n-1)} \\ Andrew Howroyd, Jul 31 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 25 2024
EXTENSIONS
a(7) onwards from Andrew Howroyd, Jul 31 2024
STATUS
approved