OFFSET
2,2
COMMENTS
The directed graphs in this sequence need not be connected, but each node must have out-degree 2. - Sean A. Irvine, Apr 09 2015
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..50
S. A. Choudum and K. R. Parthasarathy, Semi-regular relations and digraphs, Nederl. Akad. Wetensch. Proc. Ser. A. {75}=Indag. Math. 34 (1972), 326-334.
Steve Huntsman, Generalizing cyclomatic complexity via path homology, arXiv:2003.00944 [cs.SE], 2020.
Sean A. Irvine, Illustration of A003286(3).
MATHEMATICA
permcount[v_] := Module[{m = 1, s = 0, k = 0, t}, For[i = 1, i <= Length[v], i++, t = v[[i]]; k = If[i > 1 && t == v[[i - 1]], k + 1, 1]; m *= t*k; s += t]; s!/m];
edges[v_, k_] := Product[SeriesCoefficient[Product[g = GCD[v[[i]], v[[j]]]; (1 + x^(v[[j]]/g) + O[x]^(k + 1))^g, {j, 1, Length[v]}], {x, 0, k}], {i, 1, Length[v]}];
a[n_] := Module[{s = 0}, Do[s += permcount[p]*edges[p, 2], {p, IntegerPartitions[n]}]; s/n!];
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
a(7)-a(9) from Sean A. Irvine, Apr 11 2015
Terms a(10) and beyond from Andrew Howroyd, Sep 13 2020
STATUS
approved