TY  - JOUR
TI  - Some group actions and Fibonacci numbers
AB  - The Fibonacci sequence has many interesting properties and studied by many mathematicians. The terms of this sequence appear in nature and is connected with combinatorics and other branches of mathematics. In this paper, we investigate the orbit of a special subgroup of the modular group. TakingTc:=(c2+c+1−cc21−c)∈Γ0(c2), c∈Z, c≠0,Tc:=(c2+c+1−cc21−c)∈Γ0(c2), c∈Z, c≠0,we determined the orbit {Trc(∞):r∈N}.{Tcr(∞):r∈N}. Each rational number of this set is the form Pr(c)/Qr(c),Pr(c)/Qr(c), where Pr(c)Pr(c) and Qr(c)Qr(c) are the polynomials in Z[c]Z[c]. It is shown that Pr(1)Pr(1) and Qr(1)Qr(1) the sum of the coefficients of the polynomials Pr(c)Pr(c) and Qr(c)Qr(c) respectively, are the Fibonacci numbers, where $P_{r}(c)=sum limits_{s=0}^{r}(begin{array}{c}2r-s send{array}) c^{2r-2s}+sum limits_{s=1}^{r}(begin{array}{c}2r-s s-1end{array}) c^{2r-2s+1}$andQr(c)=r∑s=1(2r−ss−1)c2r−2s+2Qr(c)=∑s=1r(2r−ss−1)c2r−2s+2
AU  - Şanlı, zeynep
DO  - 10.31801/cfsuasmas.939096
PY  - 2022
JO  - Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
VL  - 71
IS  - 1
SN  - 1303-5991
SP  - 273
EP  - 284
DB  - TRDizin
UR  - http://search/yayin/detay/511698
ER  -