A058831 Number of labeled n-node 4-valent graphs containing two nonadjacent double edges.

0, 0, 0, 0, 3, 30, 405, 10080, 369180, 17959158, 1092909510, 81043601760, 7195434965235, 753877707936210, 92048844661576803, 12957249486666966390, 2083048648390795634640, 379312444955136162744540

Offset: 0

Author

N. J. A. Sloane, Jan 05 2001

Keywords

• nonn
• easy

Comments

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

References

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

Crossrefs

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

Programs

Maple

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

Formula

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

Extensions

More terms from Emeric Deutsch, Jan 26 2005