OFFSET
0,3
COMMENTS
Size of binary tree = number of internal nodes.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..12
Cyril Banderier, On the sum of the sizes of binary subtrees of a perfect binary tree, personal note, 2000.
FORMULA
a(n) = B'_n(1) where B_{n+1}(x) = 1 + x*B_n(x)^2.
From Alois P. Heinz, Jul 12 2019: (Start)
a(n) = Sum_{k=0..2^n-1} (2^n-1-k) * A309049(2^n-1,k).
a(n) = A309052(2^n-1). (End)
MAPLE
B:= proc(n) B(n):= `if`(n<0, 0, expand(1+x*B(n-1)^2)) end:
a:= n-> subs(x=1, diff(B(n), x)):
seq(a(n), n=0..9); # Alois P. Heinz, Jul 12 2019
MATHEMATICA
B[n_] := If[n<0, 0, Expand[1+x*B[n-1]^2]];
a[n_] := D[B[n], x] /. x -> 1;
Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Oct 13 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cyril Banderier, Jun 09 2000
EXTENSIONS
a(0) changed to 0 by Alois P. Heinz, Jul 12 2019
STATUS
approved