[seqfan] A076725 independent sets recurrence constant

[Kevin Ryde]

In A076725, Vaclav Kotesovec notes limit c2 * c1^(2^n).  Factor
c2=A263719 is clear.  Where would I learn more about the power
part c1=1.289751..?  Is it harder, or did I miss something easy?

I suppose it's limit of b(n) = a(n)^(1/2^n) going something like
b(n) = ( b(n-1)^(2^n) + b(n-2)^(2^n) )^(1/2^n) starting 1, 1.
Almost successive power means, but without factor 1/2 ...