  It is shown that the unique representation of positive integers in terms of
tribonacci numbers and the unique representation in terms of iterated A, B and
C sequences defined from the tribonacci word are equivalent. Two auxiliary
representations are introduced to prove this bijection. It will be established
directly on a node and edge labeled tribonacci tree as well as formally. A
systematic study of the A, B and C sequences in terms of the tribonacci word is
also presented.
