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%I #23 Oct 09 2016 03:16:01
%S 0,1,1,2,1,4,6,4,17,32,44,60,70,184,476,872,1553,2720,4288,6312,9004,
%T 11992,14372,15400,14630,11968,8104,4376,1820,560,120,16,1
%N Shapes of height-balanced AVL trees of height at most 5 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 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 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F a(n) = Sum_{h=0..5} A143897(h,n). - _Alois P. Heinz_, Mar 17 2013
%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,0,5), z,n) end: seq(a(n), n=0..32); # _Alois P. Heinz_, Aug 27 2008
%t a[n_] := Module[{B, z}, B[x_, y_, d_] := If[d >= 1, x+B[x^2+2*x*y, x, d-1], x]; Coefficient[B[z, 0, 5], z, n]]; Table[a[n], {n, 0, 32}] (* _Jean-François Alcover_, Feb 24 2015, after _Alois P. Heinz_ *)
%Y Cf. A006265, A143897.
%K nonn,fini,full
%O 0,4
%A _N. J. A. Sloane_.
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