1997 AHSME Problem 30

For positive integers n, denote D(n) by the number of pairs of different adjacent digits in the binary (base two) representation of n. For example, D(3) = D(11_{2}) = 0, D(21) = D(10101_{2}) = 4, and D(97) = D(1100001_{2}) = 2. For how many positive integers less than or equal to 97 does D(n) = 2?

\textbf{(A)}\ 16\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 26\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 35

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.