  We develop a discrete-time version of the blended dynamics theorem for the
use of designing distributed computation algorithms. The blended dynamics
theorem enables to predict the behavior of heterogeneous multi-agent systems.
Therefore, once we get a blended dynamics for a particular computational task,
design idea of node dynamics for individual heterogeneous agents can easily
occur. In the continuous-time case, prediction by blended dynamics was enabled
by high coupling gain among neighboring agents. In the discrete-time case, we
propose an equivalent action, which we call multi-step coupling in this paper.
Compared to the continuous-time case, the blended dynamics can have more
variety depending on the coupling matrix. This benefit is demonstrated with
three applications; distributed estimation of network size, distributed
computation of the PageRank, and distributed computation of the degree sequence
of a graph, which correspond to the coupling by doubly-stochastic,
column-stochastic, and row-stochastic matrices, respectively.
