In English, the word buffalo can be used as a verb, a common noun, or a place name. This leads to a linguistic puzzle where "Buffalo buffalo buffalo... buffalo." with n buffalos can be interpreted as a meaningful sentence. However, these sentences may not have a unique interpretation. Let b denote the number of ways to interpret the sentence, and take bo = b = 1. The sequence satisfies the recurrence n-2 bn = bobn2 + bbn3 + b2bn4 + + bn-2b0 = bkbn-2-k- Find a generating function for b that does not contain an infinite series. k=0 Use your generating function to find br, where r is the last two digits of your student number.