scholarly journals Some binomial-sum identities for the generalized bi-periodic Fibonacci sequences

2020 ◽  
Vol 26 (1) ◽  
pp. 199-208
Author(s):  
Ho-Hon Leung ◽  
Keyword(s):  
Binomial Sum ◽  
Fibonacci Sequences

Polynomial values in Fibonacci sequences

2020 ◽  
Vol 13 (4) ◽  
pp. 597-605
Author(s):  
Adi Ostrov ◽  
Danny Neftin ◽  
Avi Berman ◽  
Reyad A. Elrazik
Keyword(s):  
Fibonacci Sequences

Nature-Inspired Quasicrystal SRG Using Fibonacci Sequences in Photo-Reconfiguration on Azo Polymer Films

2018 ◽  
Vol 26 (11) ◽  
pp. 1042-1047 ◽  
Author(s):  
Kang-Han Kim ◽  
Kuk Young Cho ◽  
Yong-Cheol Jeong
Keyword(s):  
Polymer Films ◽  
Azo Polymer ◽  
Fibonacci Sequences

scholarly journals Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes

10.37236/1052 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Brad Jackson ◽  
Frank Ruskey
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Binary Trees ◽  
Integer Sequences ◽  
Number Of Leaves ◽  
Online Encyclopedia ◽  
Fibonacci Sequences ◽  
Infinite Sequences

We consider a family of meta-Fibonacci sequences which arise in studying the number of leaves at the largest level in certain infinite sequences of binary trees, restricted compositions of an integer, and binary compact codes. For this family of meta-Fibonacci sequences and two families of related sequences we derive ordinary generating functions and recurrence relations. Included in these families of sequences are several well-known sequences in the Online Encyclopedia of Integer Sequences (OEIS).

scholarly journals An operational calculus model for the central difference and exponential-trigonometric and hyperbolic fibonacci sequences

2018 ◽  
Vol 214 (3) ◽  
pp. 39-62
Author(s):  
Hubert Wysocki
Keyword(s):  
Operational Calculus ◽  
Difference Model ◽  
Central Difference ◽  
Fibonacci Sequences

Abstract In the paper, there has been constructed such a non-classical Bittner operational calculus model, in which the derivative is understood as a central difference Dn{x(k)}:= {x(k+n)–x(k-n)}. The discussed model has been generalized by considering the operation Dn,b{x(k)}:= {x(k+n)–bx(k-n)}, where b∈𝕔\{0}. In the D1-difference model exponential-trigonometric and hyperbolic Fibonacci sequences have been introduced.

Fibonacci Sequences

1972 ◽  
pp. 242-256
Author(s):  
Gerald Berman ◽  
K.D. Fryer
Keyword(s):  
Fibonacci Sequences
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