Some Problems Concerning Recurrence Sequences

There are questions about recurrence sequences that seem to crop up again and again. Plainly, though their answers are well known they are not known well. We endeavour to explain these answers in context so that they may become more widely known. The sequence 0,1,-1,2,-2,..., in which each integer occurs exactly once, is a recurrence sequence; that is, it satisfies a linear, homogeneous recurrence relation with constant coefficients, namely,