A003286 Number of semi-regular digraphs (with loops) on n unlabeled nodes with each node having out-degree 2. (Formerly M4441)

1, 7, 66, 916, 16816, 373630, 9727010, 289374391, 9677492899, 359305262944, 14663732271505, 652463078546373, 31435363120551013, 1630394318463367718, 90570555840053284171, 5365261686125108336540, 337616338011820295406352, 22490263897737210321234701, 1581153614004788257326876764

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!];
Table[a[n], {n, 2, 20}] (* Jean-François Alcover, Jul 20 2022, after Andrew Howroyd in A259471 *)

Crossrefs

Column k=2 of A259471.

Cf. A129524.

Sequence in context: A185181 A024395 A215077 * A244602 A223889 A197744

Adjacent sequences: A003283 A003284 A003285 * A003287 A003288 A003289

Keyword

nonn,nice

Author

N. J. A. Sloane

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