Number of Trees in a Cascade of 2-Port Networks

Recurrence formulas for the numbers of trees, port terminal-pair 2-trees, and terminal 3-trees in a cascade of nonidentical 2-port networks are presented in this paper. They are derived from counting series which provide a clear insight, not apparent from the recurrence formulas themselves, into the composition of the various tree structures. These formulas and series reduce readily to the simpler forms which pertain when the networks in the cascade are identical, confirming certain recurrence formulas presented previously by Gruszczynski for this special case.