Search: id:A002785
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%I A002785 M0375 N0141
%S A002785 2,2,8,12,88,176,2752,8784,279968,1492288,95458560,872687552,
%T A002785 111698291584,1787154671104,457509297625088,13013584213369088,
%U A002785 6662951988432581120,341143107490935724032,349330527429800077778944
%N A002785 Number of self-complementary oriented graphs with n nodes.
%C A002785 Farrugia's Chapter 8 on enumeration of self-complementary and self-converse 
               graphs and digraphs contains many explicit formulas as well as an 
               in-depth discussion of the literature on this subject. - Pab Ter 
               (pabrlos2(AT)yahoo.com), Oct 22 2005
%D A002785 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002785 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002785 Sridharan, M. R.; Self-complementary and self-converse oriented graphs. 
               Nederl. Akad. Wetensch. Proc. Ser. A 73=Indag. Math. 32 1970 441-447.
%H A002785 Farrugia, Alastair; <a href="http://members.lycos.co.uk/afarrugia/sc-graph.html">
               Self-complementary graphs and generalizations: a comprehensive reference</
               a>, M.Sc. Thesis, University of Malta, August 1999.
%F A002785 a(2n) = sum_{j partition of n & jk=0 if k even} [ prod_{k} 2^(k*jk^2-jk) 
               * prod_{r<t} 2^(2*gcd(r, t)*jr*jt) / prod_{k} k^jk*jk! ]; a(2n+1) 
               = sum_{j partition of n & jk=0 if k even} [ prod_{1<=r, t<=n} 2^(gcd(r, 
               t)*jr*jt) / prod_{k} k^jk*jk! ] - Pab Ter (pabrlos2(AT)yahoo.com), 
               Oct 22 2005
%p A002785 with(combinat, partition): j:=proc(p) local k, jpart: jpart:=[seq(0,k=1..max(op(p)))]: 
               for k from 1 to nops(p) do jpart[p[k]]:=jpart[p[k]]+1 od: RETURN(jpart): 
               end; numeven:=jtot->2^add(add((2*igcd(r,t)*jtot[r]*jtot[t]),r=1..t-1)+(t*jtot[t]^2-jtot[t]),
               t=1..nops(jtot)); numodd:=jtot->mul(mul(2^(igcd(r,t)*jtot[r]*jtot[t]),
               r=1..nops(jtot)),t=1..nops(jtot));den:=jtot->mul(k^jtot[k]*jtot[k]!,
               k=1..nops(jtot)); testj:=proc(jtot) local i: for i from 1 to floor(nops(jtot)/
               2) do if(jtot[2*i]<>0) then RETURN(0) fi od: RETURN(1) end; teven:=proc(n) 
               local s,part,k,p,jtot: s:=0: part:=partition(n): for k from 1 to 
               nops(part) do p:=part[k]: jtot:=j(p): if testj(jtot)=1 then s:=s+numeven(jtot)/
               den(jtot) fi od:RETURN(s): end; todd:=proc(n) local s,part,k,p,jtot: 
               s:=0: part:=partition(n): for k from 1 to nops(part) do p:=part[k]: 
               jtot:=j(p): if testj(jtot)=1 then s:=s+numodd(jtot)/den(jtot) fi 
               od:RETURN(s): end; seq(op([todd(n),teven(n+1)]),n=1..12); (Pab Ter)
%Y A002785 Sequence in context: A089248 A006663 A094941 this_sequence A045686 A045677 
               A005633
%Y A002785 Adjacent sequences: A002782 A002783 A002784 this_sequence A002786 A002787 
               A002788
%K A002785 nonn,nice,easy
%O A002785 3,1
%A A002785 N. J. A. Sloane (njas(AT)research.att.com).
%E A002785 More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 22 2005

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