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

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

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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.

Crossrefs

Column k=3 of A259471.

Cf. A003286, A185193.

Programs

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 *)

Extensions

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

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