A005535 Number of semi-regular digraphs (with loops) on n unlabeled nodes with each node having out-degree 3. (Formerly M5081)

1, 19, 916, 91212, 12888450, 2411213698, 575737451509, 171049953499862, 61944438230597774, 26879022100485977540, 13773587720396658214925, 8231894671550187551622795, 5676740663627528580559535893, 4474748487205893704072253926113

Offset

3,2

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 = 3..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.

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, 3], {p, IntegerPartitions[n]}]; s/n!];
Table[a[n], {n, 3, 20}] (* Jean-François Alcover, Jul 20 2022, after Andrew Howroyd in A259471 *)

Crossrefs

Column k=3 of A259471.

Cf. A003286, A185193.

Sequence in context: A217826 A209353 A368789 * A171226 A247279 A192569

Adjacent sequences: A005532 A005533 A005534 * A005536 A005537 A005538

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

a(7) from Sean A. Irvine, Jul 07 2016

Terms a(8) and beyond from Andrew Howroyd, Sep 13 2020

Status

approved