Let F_n be the nth Fibonacci number.  Then Product[(1-x^F_i),{i,1,Infinity}] is a series all of whose  coefficients are either -1, 0, or 1.  The sequence of the coefficients of this series, call them a(n), is in the OEIS as A093996.  There is a reference there to a paper by Federico Ardila at http://arxiv.org/abs/math.CO/0409418 giving a proof that the coefficients are all -1, 0, or 1 as well as a number of recurrence relations for the coefficients.  I'm wondering if, with this information it is possible to characterize some (or all) of the values of the sequence.  For example, is a(F_n) always odd?