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 A002499 Number of self-converse digraphs with n nodes. (Formerly M2875 N1156) 6

%I M2875 N1156

%S 1,3,10,70,708,15224,544152,39576432,5074417616,1296033011648,

%T 604178966756320,556052774253161600,954895322019762585664,

%U 3224152068625567826724224,20610090531322819956330186112

%N Number of self-converse digraphs with n nodes.

%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 155, Table 6.6.1 (but the last entry is wrong).

%D R. W. Robinson, personal communication.

%D R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1980.

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

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Andrew Howroyd, <a href="/A002499/b002499.txt">Table of n, a(n) for n = 1..50</a> (terms 1..28 from R. W. Robinson)

%H F. Harary and E. M. Palmer, <a href="http://dx.doi.org/10.1112/S0025579300003910">Enumeration of self-converse digraphs</a>, Mathematika, 13 (1966), 151-157.

%o (PARI)

%o 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}

%o edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i],v[j])*if(v[i]*v[j]%2==0, 2, 1))) + sum(i=1, #v, v[i]\2 + if(v[i]%2==0, (v[i]-2)\4*2+1))}

%o a(n) = {my(s=0); forpart(p=n, s+=permcount(p)*2^edges(p)); s/n!} \\ _Andrew Howroyd_, Sep 18 2018

%Y Cf. A002500.

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Vladeta Jovovic_, Apr 17 2000

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Last modified October 15 22:50 EDT 2018. Contains 316252 sequences. (Running on oeis4.)