A058830 Number of labeled n-node 4-valent graphs containing a single double edge.

0, 0, 0, 0, 0, 0, 90, 3150, 131040, 6667920, 416593800, 31506454980, 2841125225400, 301392906637680, 37173926260360890, 5276692469017119150, 854273993613848327520, 156491796247034356836000

Offset

0,7

References

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

Links

Table of n, a(n) for n=0..17.

Formula

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

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(b[n], n=0..20); # A058830(n)=b[n] - Emeric Deutsch, Jan 26 2005

Crossrefs

Cf. A005815, A058831, A058832, A058833, A058834, A058835, A058836, A058837.

Sequence in context: A367458 A240426 A065950 * A013396 A013392 A013394

Adjacent sequences: A058827 A058828 A058829 * A058831 A058832 A058833

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 05 2001

Extensions

More terms from Emeric Deutsch, Jan 26 2005

Status

approved