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 A005535 Number of semi-regular digraphs (with loops) on n unlabeled nodes with each node having out-degree 3. (Formerly M5081) 2
 1, 19, 916, 91212, 12888450, 2411213698, 575737451509, 171049953499862, 61944438230597774, 26879022100485977540, 13773587720396658214925, 8231894671550187551622795, 5676740663627528580559535893, 4474748487205893704072253926113 (list; graph; refs; listen; history; text; internal format)
 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: A183473 A217826 A209353 * 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

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Last modified June 10 09:03 EDT 2023. Contains 363196 sequences. (Running on oeis4.)