I am working with a bunch of functions of the form
fn[x1_,x2_,x3_,...,xn_] := x1x2+x2x3+...+xnx1
where $n$ changes. Is there a way to create these functions efficiently, without having to explicitly define each? I'm looking for a way of declaring, say, $n=5$ and getting back
Perhaps they could be defining iteratively? Since fn and fn-1 only differ by a few monomials. I appreciate any helpo that I can get! Thanks!