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A024358 Sum of the sizes of binary subtrees of the perfect binary tree of height n. 3
0, 1, 8, 105, 6136, 8766473, 8245941529080, 3508518207951157937469961, 311594265746788494170062926869662848646207622648, 1217308491239906829392988008143949647398943617188660186130545502913055217344025410733271773705 (list; graph; refs; listen; history; text; internal format)
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

C. Banderier, On the sum of the sizes of binary subtrees of a perfect binary tree, preprint, 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

CROSSREFS

Cf. A003095, A309049, A309052.

Sequence in context: A222839 A113551 A082735 * A055406 A155632 A129278

Adjacent sequences:  A024355 A024356 A024357 * A024359 A024360 A024361

KEYWORD

easy,nonn

AUTHOR

Cyril Banderier, Jun 09 2000

EXTENSIONS

a(0) changed to 0 by Alois P. Heinz, Jul 12 2019

STATUS

approved

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Last modified September 20 16:31 EDT 2020. Contains 337265 sequences. (Running on oeis4.)