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A053588 Number of self-complementary 4-multigraphs on n nodes. 5
1, 1, 3, 16, 121, 1480, 50993, 3279685, 505641590, 152461906778, 103587671805408, 145528904385412088, 442626996609870050404, 2918362542591139744394993, 40446812392580562094804791143, 1260273961234324967695235253182680, 80686628450087709982052029871655471264 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

V. Jovovic, On the number of m-place relations (in Russian), Logiko-algebraicheskie konstruktsii, Tver, 1992, 59-66.

J. Xu, Ch. R. Wang, J. F. Wang, The theory of self-complementary k-multigraphs (in Chinese), Pure Appl. Math. [Chuncui Shuxue yu Yingyong Shuxue] 10 (1994), Special Issue, 18-22.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..50

D. Wille, Enumeration of self-complementary structures, J. Comb. Theory B 25 (1978) 143-150.

MATHEMATICA

permcount[v_] := Module[{m = 1, s = 0, t, i, k = 0}, 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[If[EvenQ[v[[i]]*v[[j]]], GCD[v[[i]], v[[j]]], 0], {i, 2, Length[v]}, {j, 1, i - 1}] + Sum[If[EvenQ[v[[i]]], 2 Quotient[v[[i]], 4], 0], {i, 1, Length[v]}];

a[n_] := Module[{s = 0}, Do[s += permcount[p]*5^edges[p], {p, IntegerPartitions[n]}]; s/n!];

a /@ Range[1, 20] (* Jean-Fran├žois Alcover, Sep 22 2019, 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, if(v[i]*v[j]%2==0, gcd(v[i], v[j])))) + sum(i=1, #v, if(v[i]%2==0, v[i]\4*2))}

a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*5^edges(p)); s/n!} \\ Andrew Howroyd, Sep 17 2018

CROSSREFS

Cf. A004102, A004104, A053420.

Sequence in context: A121629 A200793 A141625 * A295928 A035352 A159607

Adjacent sequences:  A053585 A053586 A053587 * A053589 A053590 A053591

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Jan 19 2000

EXTENSIONS

Terms a(16) and beyond from Andrew Howroyd, Sep 17 2018

STATUS

approved

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Last modified November 13 00:25 EST 2019. Contains 329083 sequences. (Running on oeis4.)