Random Fibonacci sequence

Viswanath's constant is a mathematical constant. The value of the number is 1.13198824 (approximated to 8 decimal digits)

The constant is defined as the exponential rate at which the average absolute value of a random Fibonacci sequence increases.

A "random Fibonacci sequence" is a sequence of Fibonacci numbers that have the following recursive definition.

Terminating conditions :

Failed to parse (syntax error): {\displaystyle f(0)=\left\ 1\right }

\\f(1)=1 Recursive step :

$f(n)=\left\{{\begin{matrix}fp(n),&{\mbox{with probability 0.5}}\\fm(n),&{\mbox{with probability 0.5}}\end{matrix}}\right.$

If P(X) denotes the probability of accepting the definition of the expression X for each X,

P(F(n) = FP(n)) = 0.5 and P(F(n) = FM(n)) = 0.5

where FP(n) = F(n-1) + F(n-2)

and FM(n) = F(n-1) - F(n-2)

or in other words, the decision whether to add or subtract the previous two elements of the sequence to get the third element, is taken at random with a probability of 0.5 favouring each decision (Say with a toss of a fair coin.)