cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Kevin Ryde, Oct 11 2022

Keywords

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

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).
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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