Abstract. It is proved that the generating function A(y) for the Dhar directed-site animals-enumeration problem on the simple cubic lattice is an algebraic function. This results is used to analyse the detailed critical behaviour of A(y) as y to y_c^-, where y_c=¹/₂₂(-9+5 square root 5). Next an asymptotic expansion for the total number A_n of directed lattice animals with n sites is derived. Finally, an exact closed-form expression for the generating function A(y) is given.

Print publication: Issue 19 (7 October 1989)