A036662 Shapes of height-balanced AVL trees of height at most 5 with n nodes.

0, 1, 1, 2, 1, 4, 6, 4, 17, 32, 44, 60, 70, 184, 476, 872, 1553, 2720, 4288, 6312, 9004, 11992, 14372, 15400, 14630, 11968, 8104, 4376, 1820, 560, 120, 16, 1

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full

References

• F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 239, Eq 79, A_5.

Links

• R. C. Richards, Shape distribution of height-balanced trees, Info. Proc. Lett., 17 (1983), 17-20.
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A006265, A143897.

Programs

Maple

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

Mathematica

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 *)

Formula

a(n) = Sum_{h=0..5} A143897(h,n). - Alois P. Heinz, Mar 17 2013