RECURRENCE RELATIONS FOR THE SQUARES OF THE HORADAM NUMBERS AND SOME ASSOCIATED CONSEQUENCES

Abstract

We derive recurrence relations for the squares of the Horadam
numbers w^2_n, where the Horadam sequence w_n is such that                  the numbers w_n, for n in Z, are dened recursively by w_0 = a, w_1 = b,           w_n = pw_(n-1) - qwn_(n-2), where a, b, p and q are arbitrary complex numbers with p not 0 and q not 0. Some related results emanating from the recurrence relations such as reciprocal sums, partial sums, and sums with double binomial coecients are also presented.