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%I #10 Sep 04 2017 19:25:41
%S 0,0,0,0,0,0,180,3150,105840,4740120,260366400,17411708160,
%T 1402666372800,134317686068280,15090968212259940,1966411584852664950,
%U 294177397021128260640,50080787858122187821200
%N Number of labeled n-node 4-valent graphs containing a triple edge and a double edge.
%D R. C. Read and N. C. Wormald, Number of labeled 4-regular graphs, J. Graph Theory, 4 (1980), 203-212.
%F Read and Wormald give recurrence relations involving all sequences A005815 and A058830-A058837 (see the Maple program). - _Emeric Deutsch_, Jan 26 2005
%p 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
%Y Cf. A005815, A058830, A058831, A058832, A058833, A058834, A058836, A058837.
%K nonn,easy
%O 0,7
%A _N. J. A. Sloane_, Jan 05 2001
%E More terms from _Emeric Deutsch_, Jan 26 2005
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