A new way of counting the column-convex polyominoes by perimeter

We introduce a new class of plane figures: the sequences of tailed column-convex polyominoes (for short: stapoes). Let G(x, y) and I(x, y) denote the perimeter generating functions for column-convex polyominoes and stapoes, respectively. It will be clear from the definitions that G(x, y) is a simple fraction of I(x, y). But this latter function can be DSV-computed by solving just one quadratic equation (and not a system of quadratic equations). Thus the formula for G(x, y) can be obtained with ease.