  An equivalent definition of the Fibonacci numbers is that they are the unique
sequence such that every integer can be written uniquely as a sum of
non-adjacent terms. We can view this as we have bins of length 1, we can take
at most one element from a bin, and if we choose an element from a bin we
cannot take one from a neighboring bin. We generalize to allowing bins of
varying length and restrictions as to how many elements may be used in a
decomposition. We derive conditions on when the resulting sequences have
uniqueness of decomposition, and (similar to the Fibonacci case) when the
number of summands converges to a Gaussian; the main tool in the proofs here is
the Lyaponuv Central Limit Theorem.
