The Fibonacci Cube is an interconnection network that possesses many desirable properties that are important in network design and application. The Fibonacci Cube can efficiently emulate many hypercube algorithms and uses fewer links than the comparable hypercube, while its size does not increase as fast as the hypercube. However, most Fibonacci Cubes (more than 2/3 of all) are not Hamiltonian....

Abstract In this paper, we use the properties of error estimation and analytic method to study reciprocal products bi-periodic Fibonacci sequence, Lucas m th-order linear recursive sequence.

1. A. F. Horadam. "Basic Properties of a Certain Generalized Sequence of Numbers." The Fibonacci Quarterly 3 (1965):161-75. 2. A. F. Horadam. "Complex Fibonacci Numbers and Fibonacci Quaternions." Amer. Math. Monthly 70 (1963):289-91. 3. A. L. Iakin. "Generalized Quaternions with Quaternion Components." The Fibonacci Quarterly 15 (1977):35Q-52. 4. A. L. Iakin. "Generalized Quaternions of Higher...

What is the ANZL Algorithm? It is a genuine result of our work which is theoretically and practically proved. By using the ANZL Algorithm, we can test whether a given number belongs to Lucas’s series. It can also be used to find a sequence of Lucas’s numbers, starting from any number . If a given number completes the relation , we can say that it is a Lucas number and we mark it as . From the p...

We provide three new polynomial generalizations for the Pell sequence an, also, new formulas for this sequence. An interesting relation, in terms of partitions, between the Pell and the Fibonacci sequences is given, Finally two combinatorial interpretations for the Fibonacci numbers are given by making use of the Rogers-Ramanujan identities.

A generalization of the well-known Fibonacci sequence is k?Fibonacci whose first k terms are 0,…,0,1 and each term afterwards sum preceding terms. In this paper, we find all k-Fibonacci numbers that curious (i.e., base ten representation have form a?ab?ba?a). This work continues extends prior result Trojovský, who found with a prescribed block digits, Alahmadi et al., searched for numbers, whic...

1. Robert P. Backstrom. "On the Determination of the Zeros of the Fibonacci Sequence." The Fibonacci Quarterly 4, No. 4 (1966):313-322. 2. R. D. Carmichael. "On the Numerical Factors of the Arithmetic Forms a + 3." Annals of Mathematics9 2nd Ser. 15 (1913):30-70. 3. John H. Halton. "On the Divisibility Properties of Fibonacci Numbers." The Fibonacci Quarterly 4, No. 3 (1966):217-240. 4. D.H. Le...

The Fibonacci cube Γn is the subgraph of the n-cube induced by the binary strings that contain no two consecutive 1s. These graphs are applicable as interconnection networks and in theoretical chemistry, and lead to the Fibonacci dimension of a graph. In this paper a survey on Fibonacci cubes is given with an emphasis on their structure, including representations, recursive construction, hamilt...

We introduce a natural partial order ≤ in structurally natural finite subsets of the cobweb prefabs sets recently constructed by the present author. Whitney numbers of the second kind of the corresponding subposet which constitute Stirling-like numbers‘ triangular array are then calculated and the explicit formula for them is provided. Next in the second construction we endow the set sums of pr...