Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #12 Nov 02 2017 15:50:53
%S 0,0,0,0,0,0,0,630,28560,1330560,74314800,5057098200,413836259760,
%T 40145915529720,4558576721418720,599227672837944150,
%U 90306248160926397600,15470047011889029399840,2989635481745274974582880
%N Number of labeled n-node 4-valent graphs containing two adjacent double edges.
%C In Table I of the Read-Wormald paper the c and d rows actually show double the numbers (Wormald). - _Emeric Deutsch_, Jan 26 2005
%H R. C. Read and N. C. Wormald, <a href="http://dx.doi.org/10.1002/jgt.3190040208">Number of labeled 4-regular graphs</a>, 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 21 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(d[n],n=0..21); # A058832(n)=d[n] # _Emeric Deutsch_, Jan 26 2005
%Y Cf. A005815, A058830, A058831, A058833, A058834, A058835, A058836, A058837.
%K nonn,easy
%O 0,8
%A _N. J. A. Sloane_, Jan 05 2001
%E More terms from _Emeric Deutsch_, Jan 26 2005