2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56734We propose a new method to enumerate alternating knots using a transfer matrix approach. We apply it to count numerically various objects, including prime alternating tangles with two connected components, up to order 18--22, and comment on the large-order behavior in connection with one of the authors' conjecture.24 pages. revised 08/01: numerical data updated and fits refinedMathematical PhysicsStatistical MechanicsCombinatoricstext