A simple consequence of this recursion is, that the row sums are powers of three. The root is marked with z.
Every further square is attatched as a neighbor right or above.
This paper is concerned with the enumeration of compact-rooted animals, which are animals in which the root points are consecutive. Animals which differ only by translation are considered to be equivalent. Moreover the bijection allows the compact-rooted animals to be counted according to the number of root points. The paper also contains many references to work by physicists on problems of counting animals, which arise in studying thermodynamic models for critical phenomena and phase transitions. This paper is concerned with the enumeration of compact-rooted animals, which are animals in which the root points are consecutive.