A058835 Number of labeled n-node 4-valent graphs containing a triple edge and a double edge.

0, 0, 0, 0, 0, 0, 180, 3150, 105840, 4740120, 260366400, 17411708160, 1402666372800, 134317686068280, 15090968212259940, 1966411584852664950, 294177397021128260640, 50080787858122187821200

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(g[n], n=0..20); # A058835(n)=g[n] - Emeric Deutsch, Jan 26 2005

Crossrefs

Cf. A005815, A058830, A058831, A058832, A058833, A058834, A058836, A058837.

Sequence in context: A099106 A179721 A112068 * A008432 A289318 A250146

Adjacent sequences: A058832 A058833 A058834 * A058836 A058837 A058838

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 05 2001

Extensions

More terms from Emeric Deutsch, Jan 26 2005

Status

approved