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A357702 Path length (total depths of vertices) of the rooted binary tree with Colijn-Plazzotta tree number n. 2
0, 2, 6, 10, 12, 16, 22, 18, 22, 28, 34, 20, 24, 30, 36, 38, 26, 30, 36, 42, 44, 50, 34, 38, 44, 50, 52, 58, 66, 28, 32, 38, 44, 46, 52, 60, 54, 34, 38, 44, 50, 52, 58, 66, 60, 66, 42, 46, 52, 58, 60, 66, 74, 68, 74, 82, 50, 54, 60, 66, 68, 74, 82, 76, 82, 90 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
In a rooted binary tree each vertex has 0 or 2 children.
All terms are even since each pair of 2 child vertices are at the same depth.
LINKS
Kevin Ryde, PARI/GP Code
FORMULA
a(n) = a(x) + a(y) + A064002(n) - 1, for n>=2, where x = A002024(n-1) and y = A002260(n-1).
EXAMPLE
For n=3, tree number 3 and the depth of each of its vertices is
0 root
/ \
1 1 total depths
/ \ a(3) = 0 + 1+1 + 2+2 = 6
2 2
PROG
(PARI) See links.
CROSSREFS
Cf. A357701 (vertex depths), A064002 (number of vertices).
Cf. A196047 (in Matula-Goebel).
Sequence in context: A189680 A189395 A190003 * A263309 A253913 A190789
KEYWORD
nonn,easy
AUTHOR
Kevin Ryde, Oct 11 2022
STATUS
approved

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Last modified July 18 18:59 EDT 2024. Contains 374388 sequences. (Running on oeis4.)