$x is mutated: it receives the previous call's result and becomes the next call's argument.

say join ', ', recurse_list sub ($x) { $x * 2 }, 1, 5;

outputs:

2, 4, 8, 16, 32

Perl 5:

sub recurse_list ($f, $x, $n) { 
    map { $x = $f->($x) } 1 .. $n
}

example:

#! /usr/bin/perl
sub recurse_list ($f, $x, $n) { 
    map { $x = $f->($x) } 1 .. $n
}
say join ', ', map $_->[1], 
    recurse_list
        sub ($x) {
            [ $x->[1], $x->[0] + $x->[1] ]
        },
        [1, 1], 5;

outputs:

2, 3, 5, 8, 13