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Explicit solution formulas are presented for systems of the form Exk+1 = Axk + fk
with k ∈ K, w here K ⊂ Z is a discrete interval and the pencil λE − A is regular. Different results
are obtained when one starts with an initial condition at the point k = 0 and calculates into the future (i.e., Exk+1 = Axk + fk with k ∈ N) and when one wants to get a complete solution (i.e., Exk+1 = Axk + fk with k ∈ Z).