A058833 Number of labeled n-node 4-valent graphs containing 3 double edges, a distinguished unordered pair of which are adjacent.

0, 0, 0, 3, 0, 30, 360, 6930, 196728, 8115660, 433362960, 28552545945, 2276033387760, 216132739612218, 24118774853584320, 3125242929676107240, 465357404934002231280, 78908446775174591638440

Offset

0,4

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(e[n], n=0..20); # A058833(n)=e[n] - Emeric Deutsch, Jan 26 2005

Crossrefs

Cf. A005815, A058830, A058831, A058832, A058834, A058835, A058836, A058837.

Sequence in context: A215680 A007415 A145222 * A368284 A266168 A276913

Adjacent sequences: A058830 A058831 A058832 * A058834 A058835 A058836

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 05 2001

Extensions

More terms from Emeric Deutsch, Jan 26 2005

Status

approved