In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which call ordered numbers. We determine the properties numbers including relations with Leonardo, Fibonacci, and Lucas Symmetric antisymmetric Fibonacci are used in proofs. attain some well-known identities, Binet formula, generating function for these Finally, provide illustrations identities.

For the Lucas sequence {Uk(P,Q)} we discuss the identities like the well-known Fibonacci identities. For example, the generalizations of F2k = F 2 k+1 − F 2 k−1 and F2k+1 = F 2 k+1 + F 2 k are PU2k = U 2 k+1 − QU k−1 and U2k+1 = U k+1 − QU k , respectively. We propose a new simple method for obtaining identities involving any recurrences and use it to obtain new identities involving the Fibonac...

To facilitate rapid numerical calculations of identities pertaining to Fibonacci numbers, we present each identity as a binomial sum. Mathematics Subject Classification: 05A10,11B39

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.

In this paper, we define five parameters generalization of Fibonacci numbers that generalizes Fibonacci, Pell, Modified Jacobsthal, Narayana, Padovan, k-Fibonacci, k-Pell, k-Jacobsthal and p-numbers, distance numbers, (2, k)-distance generalized (k, r)-Fibonacci in the sense by extending definition a recurrence relation with two adding three distance, simultaneously. Tiling combinatorial interp...

In this paper, we introduce a q-analog of the bi-periodic Lucas sequence, called as the q-bi-periodic Lucas sequence, and give some identities related to the q-bi-periodic Fibonacci and Lucas sequences. Also, we give a matrix representation for the q-bi-periodic Fibonacci sequence which allow us to obtain several properties of this sequence in a simple way. Moreover, by using the explicit formu...

In this paper, we introduce the h-analogue of Fibonacci numbers for non-commutative h-plane. For hh = 1 and h = 0, these are just the usual Fibonacci numbers as it should be. We also derive a collection of identities for these numbers. Furthermore, h-Binet’s formula for the h-Fibonacci numbers is found and the generating function that generates these numbers is obtained. 2000 Mathematical Subje...

In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.

We study signed differential posets, a signed version of differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance identities for partition shapes originally conjectured by Stanley, now proven in [4, 5, 7]. We show that these identities result from a signed differential poset...

We study signed differential posets, a signed version of Stanley’s differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance identities for partition shapes originally conjectured by Stanley, now proven in [3, 4, 6]. We show that these identities result from a signed differen...