A058832 Number of labeled n-node 4-valent graphs containing two adjacent double edges.

0, 0, 0, 0, 0, 0, 0, 630, 28560, 1330560, 74314800, 5057098200, 413836259760, 40145915529720, 4558576721418720, 599227672837944150, 90306248160926397600, 15470047011889029399840, 2989635481745274974582880

Offset

0,8

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

Links

Table of n, a(n) for n=0..18.

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

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 21 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(d[n], n=0..21); # A058832(n)=d[n] # Emeric Deutsch, Jan 26 2005

Crossrefs

Cf. A005815, A058830, A058831, A058833, A058834, A058835, A058836, A058837.

Sequence in context: A234245 A234241 A185849 * A366489 A225390 A061163

Adjacent sequences: A058829 A058830 A058831 * A058833 A058834 A058835

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 05 2001

Extensions

More terms from Emeric Deutsch, Jan 26 2005

Status

approved