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A309167
a(n)^2 is the least possible value at the root of a binary tree of height n where all nodes hold positive squares and all interior nodes also equal the sum of their two children.
2
1, 5, 13, 65, 97, 229, 997, 1145, 2245, 5725, 7213, 9805, 10445, 24193, 34121, 37321, 52225, 83729, 98449, 125233, 145493, 156925, 171037, 260893, 334981, 345725, 457813, 576757, 755173, 806885, 839285, 924157
OFFSET
1,2
COMMENTS
We have binary trees with the desired properties for every height n > 0:
- for n = 1: we have the following tree B_1:
1^2
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- for any n > 0, provided we have B_n, we can build a tree B_{n+1) as follows:
3^2*B_n 4^2*B_n
\ /
\ /
\ /
(5^n)^2
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- hence the sequence is well defined.
FORMULA
a(n) <= 5^(n-1).
A309228(a(n)) = n and A309228(k) < n for any k < a(n).
EXAMPLE
a(1) = 1:
1^2
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a(2) = 5:
3^2 4^2
\ /
\ /
5^2
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a(3) = 13:
3^2 4^2
\ /
\ /
5^2 12^2
\ /
\ /
13^2
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PROG
(C++) See Links section.
CROSSREFS
Sequence in context: A149574 A372383 A301634 * A272069 A018678 A149575
KEYWORD
nonn,more
AUTHOR
Rémy Sigrist, Jul 15 2019
EXTENSIONS
a(29)-a(32) from Rémy Sigrist, Nov 16 2020
STATUS
approved