… A search of the literature seems to reveal that efforts to generalize the Fibonacci sequence …
Fibonacci sequence appear to have restricted any given term to being a function (usually sum…

… the generalized Fibonacci sequences and we investigate a much broader class … sequences
which can be regarded as the generalization of many integer sequences, such as Fibonacci, …

In studying generalized Fibonacci numbers of order k> 1 defined by the conditions P•(r)= 0
for O~ r< k, F"(k)= 1, and F"(n)= L:~-1 Fk (ni) for n> k, it is necessary to consider the …

… We define k-generalized Fibonacci numbers (k;;:; 2) in such a way that for k = 2 we get the
… Fibonacci numbers. We prove several interesting facts about these k-generalized numbers …

… the generalized Fibonacci sequence {wn}={wn (a9 b; p, q)} defined by wQ= a9 wx= b; wn=
pwn_x-qwn_2(n> 2),(1.5) where a, b9 p9 and q are arbitrary complex numbers, with q^ O. The …

… the infinite sum Z^=i(l/ a^Wkn) together with certain finite sums. If we consider specializations
Wn-Un orWn=Vn, this infinite sum can be expressed in terms of the Lambert series, which …

… The Fibonacci sequence has been generalized in many ways. … The Fibonacci sequence
has been generalized in many ways, … [1] defined a further generalized Fibonacci sequence u n …

… In the more general case, we refer to F as the (a, b)-Fibonacci sequence. Where no confusion
will result, we will suppress the dependence on a and b. Thus, in every R(a, b), there is an …

… the integers that appear in different generalized Fibonacci sequences; ie, we study the
Diophantine … We consider a generalization of Fibonacci sequence called the k-generalized …

… to generalize the weighted r-generalized Fibonacci sequences with 1 < r < oo to a class of
sequences which … We call such sequences ^-generalized Fibonacci sequences. This is a new …