Multiplicative Pulsated Fibonacci Sequences Part 2
نویسندگان
چکیده
منابع مشابه
Toeplitz transforms of Fibonacci sequences
We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.
متن کاملMultiplicative Structures on Homotopy Spectral Sequences, Part I
A tower of homotopy fiber sequences gives rise to a spectral sequence on homotopy groups. In modern times such towers are ubiquitous, and most of the familiar spectral sequences in topology can be constructed in this way. A pairing of towers W∗ ∧X∗ → Y∗ consists of maps Wm ∧Xn → Ym+n which commute (on-the-nose) with the maps in the towers. It is a piece of folklore that a pairing of towers give...
متن کاملFibonacci q-gaussian sequences
The summation formula within Pascal triangle resulting in the Fi-bonacci sequence is extended to the q-binomial coefficients q-Gaussian triangles [1, 2]. 1 Pisa historical remark The Fibonacci sequence origin is attributed and referred to the first edition (lost) of " Fiber abaci " (1202) by Leonardo Fibonacci [Pisano] (see second edition from 1228 reproduced as Il Liber Abaci di Leonardo Pisan...
متن کاملFibonacci Convolution Sequences
(1-2) F<„'> £ FWFi , 1=0 However, there are some easier methods of calculation. Let the Fibonacci polynomials Fn(x) be defined by (1.3) Fn+2(x) = xFn+1(x) + Fn(x), Fo(x)~0, F7(x) = 1 . Then, since Fn(1)= Fn, the recursion relation for the Fibonacci numbers, Fn+2= Fn+i + Fn, follows immediately by taking x = I In a similar manner we may write recursion relations for {Fff^} . From (1.3), taking t...
متن کاملOn Fibonacci-Like Sequences
In this note, we study Fibonacci-like sequences that are defined by the recurrence Sk = a, Sk+1 = b, Sn+2 ≡ Sn+1 + Sn (mod n + 2) for all n ≥ k, where k, a, b ∈ N, 0 ≤ a < k, 0 ≤ b < k + 1, and (a, b) 6= (0, 0). We will show that the number α = 0.SkSk+1Sk+2 · · · is irrational. We also propose a conjecture on the pattern of the sequence {Sn}n≥k.
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: Universal Journal of Applied Mathematics
سال: 2015
ISSN: 2331-6446,2331-6470
DOI: 10.13189/ujam.2015.030501