We study Fibonacci (staircase) polyominoes, a class of column-convex polyominoes whose lower boundary is a staircase with unit vertical steps.We derive multivariate generating functions that refine Turban's Fibonacci-number enumeration by tracking additional perimeter and area parameters.The proofs use a catalytic functional equation and, in a perimeter specialization, the kernel method, leading to explicit closed forms and Catalan-number coefficient formulas.
Baril et al. (Sat,) studied this question.