LinkedIn Test Engineer- API & Services interview questions

I have applied online and the recruiter came back to me very quickly. The phone interview went well (see the first question) and I was invited for the on-site interview. The process itself and the welcome I received was top notch (you get your LinkedIn connections map printed as a gift, lunch is included as a part of the interview and your schedule is presented to you on an iPad [which you have to give up at the end] with LinkedIn profiles of all your interviewers). The coding questions were pretty general with some more difficult variations (see second question as an example) However one interviewer tried to convince me that you can put any number on the Fibonacci sequence (which you can't btw) and I have the feeling that conversation cost me the job, since she was extremely bullish on her being right.