n_0 = 1
n_i = n_(i-1) + n_(i-1)

##</code><code>##

say (1 x 5) =~ /^(1|((?1))\2)*$/

##</code><code>##

(1 x 5) =~ /^(?:(1|((?=1)(?1))\2)(?{ say length $1 }))*$/