Some combinatorial identities via k-order Fibonacci matrices
نویسندگان
چکیده
منابع مشابه
Some Identities for Fibonacci and Incomplete Fibonacci p-Numbers via the Symmetric Matrix Method
We obtain some new formulas for the Fibonacci and Lucas p-numbers, by using the symmetric infinite matrix method. We also give some results for the Fibonacci and Lucas p-numbers by means of the binomial inverse pairing.
متن کاملSome Remarks on Fibonacci Matrices
In [1], Dazheng studies Fibonacci matrices, namely matrices M such that every entry of every positive power of M is either 0 or plus or minus a Fibonacci number. He gives 40 such four-byfour matrices. In the following, we give an interpretation of these matrices, from which we give simpler proofs of several of his theorems. We also determine all two-by-two Fibonacci matrices. Let £ = e be a pri...
متن کاملSome Combinatorial and Analytical Identities
We give new proofs and explain the origin of several combinatorial identities of Fu and Lascoux, Dilcher, Prodinger, Uchimura, and Chen and Liu. We use the theory of basic hypergeometric functions, and generalize these identities. We also exploit the theory of polynomial expansions in the Wilson and Askey-Wilson bases to derive new identities which are not in the hierarchy of basic hypergeometr...
متن کاملIdentities via Bell matrix and Fibonacci matrix
In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices, such as the Stirling matrices of both kinds, the Lah matrix, and the generalized Pascal matrix. To make the results more general, the discussion is also extended to the generalized Fibonacci numbers and the corresponding matrix. Moreover, ba...
متن کاملCombinatorial Proofs of Some Identities for the Fibonacci and Lucas Numbers
We study the previously introduced bracketed tiling construction and obtain direct proofs of some identities for the Fibonacci and Lucas numbers. By adding a new type of tile we call a superdomino to this construction, we obtain combinatorial proofs of some formulas for the Fibonacci and Lucas polynomials, which we were unable to find in the literature. Special cases of these formulas occur in ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2022
ISSN: ['1586-8850', '1787-2405', '1787-2413']
DOI: https://doi.org/10.18514/mmn.2022.3683