Consider what would happen to the Fibonacci sequence if, rather than adding the previous...

Consider what would happen to the Fibonacci sequence if, rather than adding the previous two numbers to calculate the next number, we either add or subtract the two preceding numbers according to the result of a coin toss. In 1999, Divakar Viswanath studied this idea of adding an element of randomness to the Fibonacci sequence. Suppose the first two numbers in this random Fibonacci sequence are V₁ = 1 and V₂ = 1. To determine each successive number, a coin is flipped. If the result of the flip is heads, the next umber will be the sum of the previous two numbers—that is,V_n = V_n-1 + V_n-2. If the result is tails, then the next number will be the difference of the previous two numbers, that is,V_n = V_n-2 – V_n-1.

The first nine numbers in a random Fibonacci sequence are 1, 1, 0, 1, 1, 0, 1, 1, 0. What pattern of heads and tails generated the 3rd through 9^th numbers in the sequence?