September 14, 2012 You will recall that fibonacci numbers are
formed by a sequence starting with 0 and 1 where each succeeding
number is the sum of the two preceeding numbers; that is, F[n] =
F[n-1] + F[n-2] with F = 0 and F = 1. We studied fibonacci
numbers in a previous exercise. Tribonacci numbers are like
fibonacci numbers except that the starting sequence is 0, 0 and
1 and each succeeding number is the sum of the three preceeding
numbers; that is, T[n] = T[n-1] + T[n-2] + T[n-3] with T[-1] =
0, T = 0 and T = 1. The powering matrix for tribonacci numbers,
used similarly to the powering matrix for fibonacci numbers, is:
The first ten terms of the tribonacci sequence, ignoring the two
leading zeros, are 1, 1, 2, 4, 7, 13, 24, 44, 81 and 149
(A000073). Your task is to write two functions that calculate
the first n terms of the tribonacci sequence by iteration and
the nth term by matrix powering; you should also calculate the
tribonacci constant, which is the limit of the ratio between
successive tribonacci n