Two-sided generalized Fibonacci sequences.

Motivated by the study of uniqueness in finite measurement structures, we study the concept of a two-sided generalized Fibonacci sequence. Such a sequence with n >= 2 terms is an integer sequence of the form (b sub (j),...,b sub 2, b sub 1, 1,1,a sub 1, a sub 2,..., a sub k) with J+k+2 = n such that each b sub i is the sum of one or more contiguous terms immediately to its right, and each a sub i is the sum of one or more contiguous terms immediately to its left. We investigate the number t sub n of n-term two-sided generalized Fibonacci sequences; we show that t sub 1 = 1, t sub 2 = 1, t sub (n+1) = 2nt sub n - (n-1) sup 2 t sub (n-1) for n >= 2, and t sub (n+1)/ t sub n is approximately (square root n + 1/2) sup 2 for large n.