A class of Fibonacci, Lucas-like numbers

Abstract

We study the column-convex lattice animals resulting from a class of stacking of labeled squares on a single or double stair-case. The exact expressions are obtained for the number of animals with a given length and k labeled squares, their mean length and mean-square deviation. These objects are closely related to a class of inte resting numbers. We call them the Fibonacci-like number and Lucas-like number.