The number of configurations, c（n, m）, of a single chain with length n attached to a flat surface with m monomers contacting the surface is exactly enumerated. A fimction of c（n, m） about m and n is obtained. From the function, a scaling law for mean energy of chain is derived, and we estimate the critical point εc = 0.276 and the crossover exponent φ = 0.5. The free energy difference between tethered chain and free chain in dilute solution is also studied, which shows the critical adsorption point is about 0.272 for infinite long chain with φ= 0.5.
