Let [n] = {0,...,n-1}; a(n) is number of functions f:[n] -> [n] for which there exists an injection g:[n] -> [n+1] such that for j with 0 <= j < n, either g(j) = f(j) or g(j) = f(j)+1.

A028498

Let [n] = {0,...,n-1}; a(n) is number of functions f:[n] -> [n] for which there exists an injection g:[n] -> [n+1] such that for j with 0 <= j < n, either g(j) = f(j) or g(j) = f(j)+1.