A357702 Path length (total depths of vertices) of the rooted binary tree with Colijn-Plazzotta tree number n.

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

Offset: 1

Author

Kevin Ryde, Oct 11 2022

Keywords

• nonn
• easy

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.

Examples

			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
		

Links

• Kevin Ryde, PARI/GP Code

Crossrefs

Cf. A357701 (vertex depths), A064002 (number of vertices).

Cf. A002024, A002260.

Cf. A196047 (in Matula-Goebel).

Programs

PARI

\\ See links.

Formula

a(n) = a(x) + a(y) + A064002(n) - 1, for n>=2, where x = A002024(n-1) and y = A002260(n-1).