Find the first four terms of the sequence (an)n?1 with the givendefinition. Determine if they are potentially arithmetic orgeometric.
(a) an is the number of n-bit strings which have more 1’s than0’s. (Also, write down the strings for n ? 4.)
(b) an is the number of n-bit strings in which the number of 1’sis greater than or equal to the number of 0’s in every prefix. Forexample, 010111 would not qualify, since the prefix 010 has more0’s than 1’s. (Also, write down the strings for n ? 4.)
(c) an is the number of lattice paths from (0, 0) to (n, n).(Refer to Section 1.2 if you need a refresher on latticepaths.)
