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A001374 Relational systems on n nodes. Also directed 3-multigraphs with loops on n nodes.
(Formerly M3717 N1519)
5
4, 136, 44224, 179228736, 9383939974144, 6558936236286040064, 62879572771326489528942592, 8439543710699844562674685252214784, 16110027001555070629022725866559372785352704 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

W. Oberschelp, ``Strukturzahlen in endlichen Relationssystemen,'' in Contributions to Mathematical Logic (Proceedings 1966 Hanover Colloquium), pp. 199-213, North-Holland Publ., Amsterdam, 1968.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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 = 1..40

W. Oberschelp, Strukturzahlen in endlichen Relationssystemen, in Contributions to Mathematical Logic (Proceedings 1966 Hanover Colloquium), pp. 199-213, North-Holland Publ., Amsterdam, 1968. [Annotated scanned copy]

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[2*GCD[v[[i]], v[[j]]], {i, 2, Length[v]}, {j, 1, i - 1}] + Total[v];

a[n_] := (s=0; Do[s += permcount[p]*4^edges[p], {p, IntegerPartitions[n]}]; s/n!);

Array[a, 15] (* Jean-François Alcover, Jul 08 2018, after Andrew Howroyd *)

PROG

(PARI)

permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

edges(v) = {sum(i=2, #v, sum(j=1, i-1, 2*gcd(v[i], v[j]))) + sum(i=1, #v, v[i])}

a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*4^edges(p)); s/n!} \\ Andrew Howroyd, Oct 22 2017

CROSSREFS

Cf. A000595, A004105, A053468, A053516.

Sequence in context: A012052 A054052 A012070 * A229416 A155207 A201388

Adjacent sequences:  A001371 A001372 A001373 * A001375 A001376 A001377

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vladeta Jovovic, Jan 14 2000

STATUS

approved

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Last modified December 6 20:22 EST 2021. Contains 349567 sequences. (Running on oeis4.)