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A086345 Number of connected oriented graphs (i.e., connected directed graphs with no bidirected edges) on n nodes. 4
1, 1, 1, 5, 34, 535, 20848, 2120098, 572849763, 415361983540, 815590925440865, 4373589784210012634, 64535461714821630421106, 2637732191356603658136444467, 300363258297687600380548275359231 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..50

Chathura Kankanamge, Multiple Continuous Subgraph Query Optimization Using Delta Subgraph Queries, Master Maths Thesis, Univ. of Waterloo, 2018.

Eric Weisstein's World of Mathematics, Oriented Graph

FORMULA

Inverse Euler transform of A001174. - Andrew Howroyd, Nov 03 2017

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_] := Sum[GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total @ Quotient[v - 1, 2];

a1174[n_] := Module[{s = 0}, Do[s += permcount[p]*3^edges[p], {p, IntegerPartitions[n]}]; s/n!];

b = Array[a1174, 15];

mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];

EULERi[b_] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i*b[[i]] - Sum[c[[d]]*b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d]*c[[d]], {d, 1, i}]]]; Return[a]];

A086345 = EULERi[b] (* Jean-Fran├žois Alcover, Jul 06 2018, after Andrew Howroyd *)

CROSSREFS

Cf. A054941 (labeled case), A001174.

Sequence in context: A211037 A130607 A211042 * A295545 A309534 A194687

Adjacent sequences:  A086342 A086343 A086344 * A086346 A086347 A086348

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jul 16 2003

EXTENSIONS

More terms from Vladeta Jovovic, Jul 19 2003

a(0)=1 prepended by Andrew Howroyd, Sep 09 2018

STATUS

approved

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Last modified November 14 12:33 EST 2019. Contains 329114 sequences. (Running on oeis4.)