  X.S. Lin and O. Dasbach proved that the sum of the absolute value of the
second and penultimate coefficients of the Jones polynomial of an alternating
knot is equal to the twist number of the knot. In this paper we give a new
proof of their result using Khovanov homology. The proof is by induction on the
number of crossings using the long exact sequence in Khovanov homology
corresponding to the Kauffman bracket skein relation.
