OFFSET
0,3
COMMENTS
Empty external nodes are counted in determining the height of a search tree.
LINKS
EXAMPLE
a(2) = 7 = 2 + 3 + 2:
.
2 2 1
/ \ / \ / \
1 o 1 3 o 2
/ \ ( ) ( ) / \
o o o o o o o o
.
MAPLE
b:= proc(n, h) option remember; `if`(n=0, 1, `if`(n<2^h,
add(b(j-1, h-1)*b(n-j, h-1), j=1..n), 0))
end:
T:= (n, k)-> b(n, k)-`if`(k>0, b(n, k-1), 0):
a:= k-> add(T(n, k)*n, n=k..2^k-1):
seq(a(n), n=0..10);
MATHEMATICA
b[n_, h_] := b[n, h] = If[n == 0, 1, If[n < 2^h,
Sum[b[j - 1, h - 1]*b[n - j, h - 1], {j, 1, n}], 0]];
T[n_, k_] := b[n, k] - If[k > 0, b[n, k - 1], 0];
a[k_] := Sum[T[n, k]*n, {n, k, 2^k - 1}];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Apr 26 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 29 2020
STATUS
approved