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 A003286 Number of semi-regular digraphs (with loops) on n unlabeled nodes with each node having out-degree 2. (Formerly M4441) 3
 1, 7, 66, 916, 16816, 373630, 9727010, 289374391, 9677492899, 359305262944, 14663732271505, 652463078546373, 31435363120551013, 1630394318463367718, 90570555840053284171, 5365261686125108336540, 337616338011820295406352, 22490263897737210321234701, 1581153614004788257326876764 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified February 6 15:04 EST 2023. Contains 360110 sequences. (Running on oeis4.)