A058836 Number of labeled n-node 4-valent graphs containing a loop.

0, 0, 0, 0, 0, 0, 60, 1890, 77280, 3966480, 251067600, 19204305120, 1747829270880, 186823771322760, 23188769670126060, 3309132464435848050, 538177754986005214080, 98975242794632514448320

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(h[n], n=0..20); # A058836(n)=h[n] - Emeric Deutsch, Jan 26 2005

Crossrefs

Cf. A005815, A058830, A058831, A058832, A058833, A058834, A058835, A058837.

Sequence in context: A035800 A017723 A214946 * A166792 A013925 A083367

Adjacent sequences: A058833 A058834 A058835 * A058837 A058838 A058839

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 05 2001

Extensions

More terms from Emeric Deutsch, Jan 26 2005

Status

approved