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A058837 Number of labeled n-node 4-valent graphs containing a loop and a double edge. 8
0, 0, 0, 0, 0, 30, 360, 12390, 492240, 24517080, 1499961960, 111400817220, 9894176455680, 1036335934435230, 126455286914316360, 17785504207015034490, 2856590783311452576480, 519670214181036892602720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

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(i[n], n=0..20); # A058837(n)=i[n] - Emeric Deutsch, Jan 26 2005

CROSSREFS

Cf. A005815, A058830, A058831, A058832, A058833, A058834, A058835, A058836.

Sequence in context: A179717 A086864 A138441 * A042748 A202074 A251895

Adjacent sequences:  A058834 A058835 A058836 * A058838 A058839 A058840

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jan 05 2001

EXTENSIONS

More terms from Emeric Deutsch, Jan 26 2005

STATUS

approved

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Last modified October 21 20:51 EDT 2018. Contains 316428 sequences. (Running on oeis4.)