A058834 Number of labeled n-node 4-valent graphs containing a triple edge.

0, 0, 0, 0, 0, 0, 0, 420, 16800, 763560, 43142400, 2979900000, 247022123040, 24219716320800, 2774585262168720, 367448041040780700, 55728771791388696000, 9599063849925363974160, 1863895566816244057824000

Offset

0,8

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..18.

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(f[n], n=0..21); # A058834(n)=f[n] - Emeric Deutsch, Jan 26 2005

Crossrefs

Cf. A005815, A058830, A058831, A058832, A058833, A058835, A058836, A058837.

Sequence in context: A288071 A289226 A133712 * A022046 A289348 A107510

Adjacent sequences: A058831 A058832 A058833 * A058835 A058836 A058837

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 05 2001

Extensions

More terms from Emeric Deutsch, Jan 26 2005

Status

approved