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 A058835 Number of labeled n-node 4-valent graphs containing a triple edge and a double edge. 8
 0, 0, 0, 0, 0, 0, 180, 3150, 105840, 4740120, 260366400, 17411708160, 1402666372800, 134317686068280, 15090968212259940, 1966411584852664950, 294177397021128260640, 50080787858122187821200 (list; graph; refs; listen; history; text; internal format)
 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 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(g[n], n=0..20); # A058835(n)=g[n] - Emeric Deutsch, Jan 26 2005 CROSSREFS Cf. A005815, A058830, A058831, A058832, A058833, A058834, A058836, A058837. Sequence in context: A099106 A179721 A112068 * A008432 A289318 A250146 Adjacent sequences:  A058832 A058833 A058834 * A058836 A058837 A058838 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 September 24 08:31 EDT 2021. Contains 347623 sequences. (Running on oeis4.)