Random Fibonacci Sequence

Some more mathematics while I work on combining/simplifying the equations:

The Random Fibonacci Sequence was a game proposed by a mathematician several decades ago. Start with two base numbers, and flip a coin. If heads, add the two numbers, and if tails, subtract the numbers one from the other. Then toss out the oldest number and move on to the next.

The resulting function has a growth rate converging upon a constant, which was discovered in 1999 by Divakar Viswanath. It's earned the name "Viswanath's Constant" or the "Random Fibonacci Constant".

The program I ran found a surprising correlation between it and two other constants: the MRB constant (named after Marvin Ray Burns), and the ancient Euler-Mascheroni Constant. The approximate equation is:

Viswanath ~= asinh(((ln(2) + ln(5)) * ln(asin(Euler-Mascheroni))) / (ln(MRB) * ln((1 + sqrt(5))/2)))

{Euler-Mascheroni = 0.57721566490153286060651209008240243; MRB = 0.18785964246206712024851793405427323}

Or in mathematical notation:

V = lim_n→∞|a_n|^1/_n ~= sinh^-1(log_φ(10) * log_MRB(sin^-1(γ)))

{φ =^{(1 + sqrt(5))}/₂; MRB = MRB; γ = Euler-Mascheroni}

Assuming this formula is even remotely correct, a very liberal estimate of Viswanath's Constant would be:

V = lim_n→∞|a_n|^1/_n ~= 1.1319882412441814249833117871080...

Again it diverges at some point from the accepted value, and I cannot help but to feel that the equation is either highly coincidental or missing some small component, but as with the previous equations, this serves as a place to start, as only a few decimal places of Viswanath's Constant are currently known.