A058831 - OEIS

%I #10 Sep 04 2017 19:25:11

%S 0,0,0,0,3,30,405,10080,369180,17959158,1092909510,81043601760,

%T 7195434965235,753877707936210,92048844661576803,12957249486666966390,

%U 2083048648390795634640,379312444955136162744540

%N Number of labeled n-node 4-valent graphs containing two nonadjacent double edges.

%C In Table I of the Read-Wormald paper the c and d rows actually show double the numbers (Wormald). - _Emeric Deutsch_, Jan 26 2005

%D R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.

%F Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - _Emeric Deutsch_, Jan 26 2005

%p a[0]:=1: b[0]:=0: c[0]:=0: d[0]:=0: e[0]:=0: f[0]:=0: g[0]:=0: h[0]:=0: i[0]:=0: for p from 1 to 20 do a[p]:=((p-1)*(2*p-9)*a[p-1]+(2*p-8)*b[p-1]+c[p-1])/3: b[p]:=(6*p*(p-1)*a[p-1]+4*p*b[p-1]+p*d[p-1])/2: c[p]:=(6*p*(p-3)*b[p-1]+8*p*c[p-1]+4*p*d[p-1]+p*e[p-1])/4: d[p]:=p*b[p-1]+p*f[p-1]:e[p]:=(4*p*c[p-1]+4*p*d[p-1]+2*p*g[p-1]+p*(p-1)*(p-2)*a[p-3])/2:f[p]:=p*(p-1)*((4*p-8)*a[p-2]+2*b[p-2]+h[p-2])/2: g[p]:=p*(p-1)*(4*(p-3)*b[p-2]+4*c[p-2]+4*d[p-2]+2*f[p-2]+i[p-2])/2:h[p]:=p*((2*p-2)*a[p-1]+b[p-1]): i[p]:=p*((2*p-4)*b[p-1]+2*c[p-1]+2*d[p-1]+f[p-1]+h[p-1]): od: seq(c[n],n=0..20); # A058831(n)=c[n] - _Emeric Deutsch_, Jan 26 2005

%Y Cf. A005815, A058830, A058832, A058833, A058834, A058835, A058836, A058837.

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_, Jan 05 2001

%E More terms from _Emeric Deutsch_, Jan 26 2005