The present work aims to introduce and study the Gaussian Bronze Lucas number sequence. Firstly, we define numbers by extending numbers. Then, find Binet formula generating function for this We also investigate some sum formulas matrices related Finally, obtain known equalities like Catalan, Cassini d’Ocagne identities considering of

Abstract By means of the telescoping method, several summation formulae are established for arctangent function with its argument being Pell and Pell–Lucas polynomials. Numerous infinite series identities involving Fibonacci Lucas numbers included as particular cases.

is called the characteristic polynomial of the sequence U. In the case where P = -g = 1, the sequence U is the Fibonacci sequence and we denote its terms by F0, Fl9 F2, ... . Let p be an odd prime with p\Q and let e > 1 be an integer. The positive integer u = u(p) is called the rank of apparition of p in the sequence U if p\Uu and p\Um for 0 < m < u; furthermore, u = u(p) is called the period o...

Both Fibonacci and Lucas numbers can be described combinatorially in terms of 0− 1 strings without consecutive ones. In the present article we explore the occupation numbers as well as the correlations between various positions in the corresponding configurations. (2000) Mathematics Subject Classification: 11B39, 05A15

Among the most intensively studied integer sequences are the Fibonacci and Lucas sequences. Both are instances of second order recurrences [8], both satisfying sk−2+sk−1 = sk for all integers k, but where the fibonacci sequence (fi) begins with f0 = 0 and f1 = 1, the Lucas sequence (li) has l0 = 2 and l1 = 1. Several authors have recently been interested in the singular values of Toeplitz, circ...

are well known. A list of such basic identities can be found in [3]. If A ^ ±1 or B ^ 1, then w1? s^,... are nonzero by [1], and so are vx = u2lul9 v2 = M4/M2, ... . In the case A = B 1, we noted in [1] that un = 0 o 31n. IF vw = 0, then uln = i/wvw = 0; hence, 31n and un = Q, which is impossible since v~Au = 4B (cf. [3]). Thus, v0,v1? v2,... are all nonzero. We set vw! = Ilo ^ reg...

The Lucas-Kanade (LK) method is a classic tracking algorithm exploiting target structural constraints thorough template matching. Extended Lucas Kanade or ELK casts the original LK algorithm as a maximum likelihood optimization and then extends it by considering pixel object / background likelihoods in the optimization. Template matching and pixel-based object / background segregation are tied ...

We investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning relationship between sets different levels, also discuss counterpart this result for Lucas k. then use some recent arithmetic properties generalized Lucas, Pell–Lucas sequences, to define new types levels k+ k− parameter a. For these novel pseudoprime sequences basic calculate numerous associated intege...

In this article we investigate the Bernoulli numbers B̂n associated to the formal group laws whose canonical invariant differentials generate the Lucas sequences {Un} and {Vn}. We give explicit expressions for these numbers and prove analogues of Kummer congruences for them.