a(n) = number of (s(0), s(1), ..., s(n)) such that every s(i) is an integer, s(0) = 0, |s(i) - s(i-1)| = 1 for i = 1,2,3; |s(i) - s(i-1)| <= 1 for i >= 4, s(n) = 4. Also a(n) = T(n,n-4), where T is the array defined in A026082.
Conjecture: -(n-4)*(n+4)*a(n) +(4*n^2-11*n-27)*a(n-1) +(-2*n^2+29*n-24)*a(n-2) -(4*n+5)*(n-5)*a(n-3) +3*(n-5)*(n-6)*a(n-4)=0. - R. J. Mathar, Jun 23 2013