3,1

Farrugia's Chapter 8 on enumeration of self-complementary and self-converse graphs and digraphs contains a many explicit formulae as well as an in-depth discussion of the literature on this subject. - Pab Ter (pabrlos2(AT)yahoo.com), Oct 22 2005

Sridharan, M. R.; Self-complementary and self-converse oriented graphs. Nederl. Akad. Wetensch. Proc. Ser. A 73=Indag. Math. 32 1970 441-447.

Farrugia, Alastair; Self-complementary graphs and generalizations: a comprehensive reference, M.Sc. Thesis, University of Malta, August 1999.

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

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)

Adjacent sequences: A002782 A002783 A002784 this_sequence A002786 A002787 A002788

Sequence in context: A089248 A006663 A094941 this_sequence A045686 A045677 A005633

nonn,nice,easy

njas

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 22 2005