A019498 Number of 4-ary search trees on n keys.

1, 1, 1, 1, 4, 10, 20, 47, 128, 340, 868, 2275, 6188, 16922, 46112, 126613, 351568, 981622, 2747876, 7723250, 21811856, 61828886, 175752728, 500984606, 1432111244, 4104175970, 11787811340, 33926475162, 97837209036, 282662156478, 818022923184, 2371103693427

Offset

0,5

Links

Table of n, a(n) for n=0..31.

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

Maple

A:= proc(n) option remember; if n=0 then 1 else convert(series(sum(x^i, i=0..2)+ x^3*A(n-1)^4, 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[1 + x + x^2 + x^3*A[n-1]^4, {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 *)

Crossrefs

Sequence in context: A048008 A048019 A189586 * A237626 A020149 A056412

Adjacent sequences: A019495 A019496 A019497 * A019499 A019500 A019501

Keyword

nonn

Author

James Fill (jimfill(AT)jhu.edu)

Extensions

More terms from Alois P. Heinz, Aug 22 2008

Status

approved