%I A006265 M0170
%S A006265 1,1,2,1,4,6,4,17,32,44,60,70,184,476,872,1553,2720,4288,6312,9004,
%T A006265 16088,36900,82984,174374,346048,653096,1199384,2160732,3812464,
%U A006265 6617304,11307920,18978577,31327104,51931296,90400704,170054336
%N A006265 Shapes of height-balanced AVL trees with n nodes.
%C A006265 An AVL tree is a complete ordered binary rooted tree where at any node, 
               the height of both subtrees are within 1 of each other.
%D A006265 R. C. Richards, Shape distribution of height-balanced trees, Info. Proc. 
               Lett., 17 (1983), 17-20.
%D A006265 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006265 This is the limit of A_k as k->inf, see F. Bergeron, G. Labelle and P. 
               Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, 
               p. 239, Eq 79.
%H A006265 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%H A006265 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A006265 G.f.: A(x)=B(x, 0) where B(x, y) satisfies B(x, y)=x+B(x^2+2xy, x).
%p A006265 a := proc(n::posint) local B; B := proc (x,y,d,a,b) if a+b<=d then x+B(x^2+2*x*y, 
               x, d, a+b, a) else x fi end; coeff (B (z,0,n,1,1),z,n) end; seq (a(n), 
               n=1..36); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 10 
               2008]
%Y A006265 Cf. A036662, A134306.
%Y A006265 Sequence in context: A143897 A036662 A134306 this_sequence A131452 A111104 
               A026190
%Y A006265 Adjacent sequences: A006262 A006263 A006264 this_sequence A006266 A006267 
               A006268
%K A006265 nonn
%O A006265 1,3
%A A006265 N. J. A. Sloane (njas(AT)research.att.com).
%E A006265 More terms, formula and comment from Christian G. Bower (bowerc(AT)usa.net), 
               Dec 15 1999.