Every day for the past days
Even Stevens brings home his groceries in a plastic bag. He stores these
plastic bags in a cupboard. He either puts the plastic bag into the
cupboard with the rest, or else he takes an even number
of the existing bags (which may either be empty or previously filled
with other bags themselves) and places these into the current bag.
After days there are possible packings and if the bags are
numbered (oldest), , they are:
Four empty bags,
and inside empty,
and inside empty,
and inside empty,
and inside empty.
Note that inside is invalid because every bag must
contain an even number of bags.
Define to be the number of
possible packings of bags. Hence
. You are also given .