A combinatorial reduction of the Frobenius problem to an optimization task produces explicit formulas for g(A), n(A), and s(A) on special sequences and applies MacMahon's partition analysis to count representations.
Greenberg, Solution to a linear diophantine equation for nonnegative integers , J
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A Combinatorial Approach to Frobenius Numbers of Some Special Sequences (Complete Version)
A combinatorial reduction of the Frobenius problem to an optimization task produces explicit formulas for g(A), n(A), and s(A) on special sequences and applies MacMahon's partition analysis to count representations.