The temperatures of the n-th active elements of the LPIEC can be described here by the

recurrence relation [10]:

This binary sequence is generated using the

recurrence relation of the form as in the equation 1.

Firstly, we find a

recurrence relation for the generating function [F.

We remark that the coefficients of a, b, c in the leftmost color (as well as in the middle and in the rightmost colors), satisfy a

recurrence relation similar to the one [x.

To compute the first few values of these numbers, the following

recurrence relation was obtained in [3]:

3), the coefficients of the three-term

recurrence relation subject to the weight function [([[pi].

Further the results are deduced for moments of order statistics and lower record values and characterization of this distribution has been considered on using conditional expectation of function of lower generalized order statistics and a

recurrence relation for single moments.

One should be tempted to use the

recurrence relation,

The sequence of Lucas polynomials is a sequence of polynomials defined by the

recurrence relationm], and satisfying the three term

recurrence relationd} avoiding words with "12" as substring is equal to a(n), a recursive sequence with initial terms a(0) = 1, a(1) = d and

recurrence relationWe consider a linear homogeneous

recurrence relation with constant coefficients