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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.)