The number of s-polymer coverings on an n x m lattice obeys the recurrence sum_{i=0}^{2s} (-1)^i binom(2s,i) a_{n-i,m-i} = 2^s (2s)! / s! .
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Regular structures of an intractable enumeration problem: a diagonal recurrence relation of monomer-polymer coverings on two-dimensional rectangular lattices
The number of s-polymer coverings on an n x m lattice obeys the recurrence sum_{i=0}^{2s} (-1)^i binom(2s,i) a_{n-i,m-i} = 2^s (2s)! / s! .