Exact results for average cluster numbers in bond percolation on lattice strips

We present exact calculations of the average number of connected clusters per site, [Formula presented], as a function of bond occupation probability [Formula presented], for the bond percolation problem on infinite-length strips of finite width [Formula presented], of the square, triangular, honeycomb, and kagomé lattices [Formula presented] with various boundary conditions. These are used to study the approach of [Formula presented], for a given [Formula presented] and [Formula presented], to its value on the two-dimensional lattice as the strip width increases. We investigate the singularities of [Formula presented] in the complex [Formula presented] plane and their influence on the radii of convergence of the Taylor series expansions of [Formula presented] about [Formula presented] and [Formula presented].