A134306 Number of shapes of height-balanced AVL trees of height at most 6 with n nodes.

0, 1, 1, 2, 1, 4, 6, 4, 17, 32, 44, 60, 70, 184, 476, 872, 1553, 2720, 4288, 6312, 9004, 16088, 36900, 82984, 174374, 346048, 653096, 1199384, 2160732, 3812464, 6617304, 11307920, 18978577, 31327104, 50882720, 80963520, 125489856, 188637520, 273984664

Offset: 0

Author

Alois P. Heinz, Aug 27 2008

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

• Alois P. Heinz, Table of n, a(n) for n = 0..64
• R. C. Richards, Shape distribution of height-balanced trees, Info. Proc. Lett., 17 (1983), 17-20.
• Wikipedia, AVL tree
• Index entries for sequences related to rooted trees

Crossrefs

Cf. A006265, A036662.

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,0,6), z,n) end: seq(a(n), n=0..64);

Mathematica

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 *)

Formula

a(n) = Sum_{h=0..6} A143897(h,n).