growing binary trees

[Simon Strandgaard]

I made up an interesting sequence:

1, 2, 3, 4, 6, 8, 10, 13, 17, 21, 26, 33, 41,
50, 62, 77, 94, 115, 142, 174, 212, 260, 319,
389, 475, 582, 711, 867, 1060, 1296


Its a binary tree where leafs is getting
added when a nodes internal counter reaches 3.





below is my slow ruby program:

class Node
  def initialize
    @n = 1
    @childs = []
  end
  def count
    @childs.inject(@n){|n,child| n + child.count}
  end
  def grow
    return @n += 1 if @n < 3
    @childs.each{|child| child.grow }
    @childs << Node.new if @childs.size < 2
  end
end

result = []
node = Node.new
30.times do |i|
  result << node.count
  node.grow
end
p result







# btw: the grow method below outputs A000071: Fibonacci numbers - 1.
def grow
  return @n += 1 if @n < 1
  @childs.each{|child| child.grow }
  @childs << Node.new if @childs.size < 2
end


# btw: the grow method below outputs A054405: Row sums of array T as in A055215.
def grow
  return @n += 1 if @n < 2
  @childs.each{|child| child.grow }
  @childs << Node.new if @childs.size < 2
end




--
Simon Strandgaard