Restricted valence site animals on the triangular lattice

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Abstract
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.

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