A259471 -id:A259471 - cp's OEIS frontend

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

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

Offset: 2

N. J. A. Sloane

The directed graphs in this sequence need not be connected, but each node must have out-degree 2. - Sean A. Irvine, Apr 09 2015

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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).

Column k=2 of A259471.

Cf. A129524.

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 *)

a(7)-a(9) from Sean A. Irvine, Apr 11 2015

Terms a(10) and beyond from Andrew Howroyd, Sep 13 2020

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

Original entry on oeis.org

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

Offset: 3

N. J. A. Sloane

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

Column k=3 of A259471.

Cf. A003286, A185193.

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 *)

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

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

cp's OEIS Frontend

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

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