The evaluation of the number of attractors in Kauffman networks by Samuelsson and Troein is generalized to critical networks with one input per node and to networks with two inputs per node and different probability distributions for update functions. A connection is made between the terms occurring in the calculation and between the more graphic concepts of frozen, nonfrozen, and relevant nodes, and relevant components. Based on this understanding, a phenomenological argument is given that reproduces the dependence of the attractor numbers on system size.