  An analytical metric of four-dimensional General Relativity, representing an
array of collinear and accelerating black holes, is constructed with the
inverse scattering method. The solution can be completely regularised from any
conical singularity, thanks to the presence of an external gravitational field.
Therefore the multi-black hole configuration can be maintained at equilibrium
without the need of string or struts. Some notable subcases such as the
accelerating distorted Schwarzschild black hole and the double distorted
C-metric are explicitly presented. The Smarr law and the thermodynamics of
these systems is studied. The Bonnor-Swaminarayan and the
Bi\v{c}\'ak-Hoenselaers-Schmidt particle metrics are recovered, through
appropriate limits, from the multi-black holes solutions.
