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

0,4

References

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

Links

Table of n, a(n) for n=0..32.

R. C. Richards, Shape distribution of height-balanced trees, Info. Proc. Lett., 17 (1983), 17-20.

Index entries for sequences related to rooted trees

Formula

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

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 *)

Crossrefs

Cf. A006265, A143897.

Sequence in context: A217299 A333340 A217300 * A134306 A006265 A131452

Adjacent sequences: A036659 A036660 A036661 * A036663 A036664 A036665

Keyword

nonn,fini,full

Author

N. J. A. Sloane.

Status

approved