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Search: id:A058837
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| A058837 |
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Number of labeled n-node 4-valent graphs containing a loop and a double edge. |
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+0
8
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| 0, 0, 0, 0, 0, 30, 360, 12390, 492240, 24517080, 1499961960, 111400817220, 9894176455680, 1036335934435230, 126455286914316360, 17785504207015034490, 2856590783311452576480, 519670214181036892602720
(list; graph; listen)
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OFFSET
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0,6
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REFERENCES
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R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.
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FORMULA
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Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 26 2005
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MAPLE
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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] (Deutsch)
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CROSSREFS
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Cf. A005815, A058830, A058831, A058832, A058833, A058834, A058835, A058836.
Sequence in context: A008656 A086864 A138441 this_sequence A042748 A022690 A020927
Adjacent sequences: A058834 A058835 A058836 this_sequence A058838 A058839 A058840
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Jan 05 2001
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 26 2005
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