*It’s the holiday time of year: so a slightly lazy post for August. Adapted from a letter published in this month’s edition of Mathematics Today …*

For anyone who’s worked in the ‘Twilight Zone’ between mathematics and computer science for any time, June’s Mathematics Today article, *Urban Maths: A Roundabout Journey* [on rounding issues in computer calculations], would have struck a distinct chord. They will have often come across situations in which mathematicians and computer scientists don’t quite see eye to eye. The following, fairly well-known, combinatorial exercise is another good example.

How many *ordered* ways are there of summing contributions of *1* and *2* to a given integer, *n*? So, for example, *1+1+2+1+1* and *2+2+2* are two of the *13* different ways of making *6*. Call this number *f(n)* so that, in this example, *f(6) = 13*.

The standard combinatorial approach is to consider the first term. The only two options, *1* (leaving *n-1* to make) and *2* (leaving *n-2*) lead readily to the recurrence relation *f(n) = f(n-1) + f(n-2)*. Easy enough, yes, but the interesting question now is *what to do with it?*