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Search: id:A058835
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| A058835 |
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Number of labeled n-node 4-valent graphs containing a triple edge and a double edge. |
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+0
8
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| 0, 0, 0, 0, 0, 0, 180, 3150, 105840, 4740120, 260366400, 17411708160, 1402666372800, 134317686068280, 15090968212259940, 1966411584852664950, 294177397021128260640, 50080787858122187821200
(list; graph; listen)
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OFFSET
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0,7
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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(g[n], n=0..20); # A058835(n)=g[n] (Deutsch)
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CROSSREFS
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Cf. A005815, A058830, A058831, A058832, A058833, A058834, A058836, A058837.
Sequence in context: A154672 A099106 A112068 this_sequence A008432 A008378 A035830
Adjacent sequences: A058832 A058833 A058834 this_sequence A058836 A058837 A058838
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), 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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