I think you're aware of this solution for anbncn but I'll post it anyway(it uses ??{} blocks and ?{} and is a Perl regex). 
$r = qr/^(a+b)(?{ $a = -1+length $^N; })(??{ $b=$a-1;"(b{$b})" })(??{ 
+"(c{$a})" })/x;

sub test {
        print
        $_[0] =~ $r
        ? "matched\n"
        : "not matched\n";
}

test "aaabbbccc";
test "aaaabbbccc";
test "aaaabbbbccc";
test "aaaabbbbcccc";
test "aabbbbcccc";
test "abc";
test "aabbcc";

[download]
Result on Perl v5.8.8: 
matched
not matched
not matched
matched
not matched
matched
matched

[download]

In reply to Re^4: check for square-number with a regex by spx2
in thread check for square-number with a regex by Ratazong

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