 If "a" and "b" represent two different materials or atomic bond lengths, the structure corresponding to a Fibonacci string is a Fibonacci quasicrystal, an aperiodic quasicrystal structure with unusual spectral properties.A convolved Fibonacci sequence is obtained applying a convolution operation to the Fibonacci sequence one or more times.Specifically, define

and

The first few sequences are

The sequences can be calculated using the recurrence

The generating function of the formula_75th convolution is 

The sequences are related to the sequence of Fibonacci polynomials by the relation
where formula_112 is the formula_75th derivative of formula_114.