A338971 Linear representation of the complete labeled binary trees of all integer heights, where the nodes at level i, 0 <= i <= n, of a binary tree with height n are labeled with the number n-i.

0, 1, 0, 0, 2, 1, 1, 0, 0, 0, 0, 3, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,5

Links

Table of n, a(n) for n=0..104.

Example

First few terms where each line represents a complete binary tree:
  n=0:  0
  n=1:  1 0 0
  n=2:  2 1 1 0 0 0 0
  n=3:  3 2 2 1 1 1 1 0 0 0 0 0 0 0 0
  n=4:  4 3 3 ...
Using this representation, the first row r(0) is given by [0]; row(n+1) is given by adding 1 to each member of r(n) and appending 2^(n+1) 0's: r(0) = [0], r(n+1) = [ i + 1 | i <- r(n) ] ++ [ 0 | i <- [1..2^(n+1)] ].

Prog

(Haskell)
concat [ tree n | n <- [0..] ]
  where tree 0 = [0]
        tree n = [ i+1 | i <- tree (n-1) ] ++ [ 0 | i <- [1..2^n] ]

Crossrefs

Cf. A290255, A126646 (row lengths).

Sequence in context: A259829 A035185 A339659 * A244600 A288558 A362831

Adjacent sequences: A338968 A338969 A338970 * A338972 A338973 A338974

Keyword

nonn,tabf

Author

Marc van Dongen, Dec 18 2020

Status

approved