%I #29 Jul 14 2024 12:26:26
%S 0,1,1,2,1,4,6,4,17,32,44,60,70,184,476,872,1553,2720,4288,6312,9004,
%T 16088,36900,82984,174374,346048,653096,1199384,2160732,3812464,
%U 6617304,11307920,18978577,31327104,50882720,80963520,125489856,188637520,273984664
%N Number of shapes of height-balanced AVL trees of height at most 6 with n nodes.
%D F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 239, Eq 79, A_5.
%H Alois P. Heinz, <a href="/A134306/b134306.txt">Table of n, a(n) for n = 0..64</a>
%H R. C. Richards, <a href="http://dx.doi.org/10.1016/0020-0190(83)90085-6">Shape distribution of height-balanced trees</a>, Info. Proc. Lett., 17 (1983), 17-20.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/AVL_tree">AVL tree</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F a(n) = Sum_{h=0..6} A143897(h,n).
%p a:= proc(n) local B,z; B:= proc(x,y,d) if d>=1 then x+B(x^2+2*x*y, x,d-1) else x fi end; coeff(B(z,0,6), z,n) end: seq(a(n), n=0..64);
%t a[n_] := Module[{B, z}, B[x_, y_, d_] := B[x, y, d] = If[d >= 1, x+B[x^2+2*x*y, x, d-1], x]; Coefficient[B[z, 0, 6], z, n]]; Table[a[n], {n, 0, 64}] (* _Jean-François Alcover_, Mar 05 2014, after _Alois P. Heinz_ *)
%Y Cf. A006265, A036662.
%K nonn,fini,full
%O 0,4
%A _Alois P. Heinz_, Aug 27 2008