RESTRICTED VALENCE SITE ANIMALS ON THE TRIANGULAR LATTICE

Exact values of the numbers of connected clusters of n sites, each site having valence no larger than v, are presented for the triangular lattice for v=2,3,4 and 5 for small values of n. Assuming a plausible asymptotic form for the dependence of these numbers on n and v the authors show, using series analysis techniques, that the exponent characterising the dominant singularity in the generating function has the same value for all v>or=3 but a different value for v=2.