Search: id:A000226
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%I A000226 M2668 N1066
%S A000226 1,1,3,7,18,44,117,299,793,2095,5607,15047,40708,110499,301541,
%T A000226 825784,2270211,6260800,17319689,48042494,133606943,372430476,
%U A000226 1040426154,2912415527,8167992598,22947778342,64577555147
%N A000226 Number of n-node unlabeled connected graphs with one cycle of length 
               3.
%C A000226 Number of rooted trees where root has degree 3. - Christian Bower (bowerc(AT)usa.net)
%D A000226 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000226 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000226 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               150.
%H A000226 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A000226 G.f.: (r(x)^3+3*r(x)*r(x^2)+2*r(x^3))/6 where r(x) is g. f. for rooted 
               trees (A000081).
%p A000226 b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), 
               k=1..n-1)/(n-1) fi end: s:= proc(n,k) option remember; add(b(n+1-j*k), 
               j=1..iquo(n,k)) end: B:= proc(n) option remember; unapply (add (b(k)*x^k, 
               k=1..n),x) end: a:= n-> coeff (series ((B(n-2)(x)^3+ 3*B(n-2)(x)* 
               B(n-2)(x^2)+ 2*B(n-2)(x^3))/6, x=0, n+1), x,n): seq (a(n), n=3..29); 
               [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
%Y A000226 Sequence in context: A129921 A036670 A027967 this_sequence A036883 A114713 
               A116413
%Y A000226 Adjacent sequences: A000223 A000224 A000225 this_sequence A000227 A000228 
               A000229
%K A000226 nonn,nice
%O A000226 3,3
%A A000226 N. J. A. Sloane (njas(AT)research.att.com).
%E A000226 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 19 2000

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