A019500 Number of 6-ary search trees on n keys.

1, 1, 1, 1, 1, 1, 6, 21, 56, 126, 252, 492, 1062, 2667, 7252, 19509, 49824, 121019, 286974, 687384, 1702308, 4357383, 11322408, 29307458, 74897808, 189349041, 477491356, 1211349276, 3103673406, 8017385416, 20780391882, 53812468392, 138999941172, 358502419242

Offset: 0

Author

James Fill (jimfill(AT)jhu.edu)

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..700
• J. A. Fill and R. P. Dobrow, The number of m-ary search trees on n keys, Combin. Probab. Comput. 6 (1997), 435-453.
• Index entries for sequences related to rooted trees

Programs

Maple

A:= proc(n) option remember; if n=0 then 1 else convert(series(
      add(x^i, i=0..4)+ x^5*A(n-1)^6, x=0,n+1), polynom) fi
    end:
a:= n-> coeff(A(n), x, n):
seq(a(n), n=0..40);  # Alois P. Heinz, Aug 22 2008

Mathematica

A[n_] := A[n] = If[n==0, 1, Series[Sum[x^i, {i, 0, 4}] + x^5*A[n-1]^6, {x, 0, n+1}] // Normal]; a[n_] := Coefficient[A[n], x, n]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 19 2016, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n / n^(3/2), where d = 2.705312740243..., c = 0.3835479397... . - Vaclav Kotesovec, Sep 06 2014

Extensions

More terms from Alois P. Heinz, Aug 22 2008