Temperley's triangular lattice compact cluster model: exact solution in terms of the q series

Temperley's model (1952) of self-supporting stackings of circles in a triangular lattice array against a line wall is solved exactly in terms of q hypergeometric functions. For N circles, the number of different configurations is described by the large-N asymptotic law A lambda ^N, with A=0.312 36. . . and lambda =1.735 66. . . .