The decimal number corresponding to a sequence of n binary digits a0, a1, . . . , an−1, where each ai is either 0 or 1, is defined to be
a020 +a121+· · ·+an−12n−1
For example, the sequence 0 1 1 0 is equal to 6 (= 0 · 20 +1 · 21 +1 · 22 +0 · 23). Suppose a fair coin is tossed nine times. Replace the resulting sequence of H’s and T’s with a binary sequence of 1’s and 0’s (1 for H, 0 for T). For how many sequences of tosses will the decimal corresponding to the observed set of heads and tails exceed 256?