Araştırma Makalesi
Yıl 2024,
Cilt: 2 Sayı: 2, 87 - 94, 31.12.2024
Öz
Kaynakça
- W. R. Spickerman, 1982, Binet’s formula for the Tribonacci Sequence, The Fibonacci Quarterly, 10, 118-120. google scholar
- T. Komatsu, 2018, Convolution Identities for Tribonacci Numbers, Ars Combinatoria, CXXXVI, 199-210. google scholar
- R.Frontczak, 2018, Convolutions for Generalized Tribonacci Numbers and Related Results, International Journal of Mathematical Analysis, 12(7), 307-324. google scholar
- A. G. Shannon,1972, Iterative Formulas Associated with Generalized Third-Order Recurrence Relations. SIM J. Appl. Math., 23(3), 364-367. google scholar
- M. Feinberg, 1963, Iterative Formulas Associated with Generalized Third-Order Recurrence Relations. The Fibonacci Quarterly, 1(1), 71-74. google scholar
- M. Elia, 2001, Derived Sequences, The Tribonacci Recurrence and Cubic Forms. The Fibonacci Quarterly,39(2), 107-109. google scholar
- A. C. F. Bueno, 2015, Notes on Number Theory and Discrete Mathematics,The Fibonacci Quarterly, 21, 67-69. google scholar
- M. Catalani, 2002, Identities for Tribonacci-related sequences, Combinatorics, Available from: https://arxiv.org/pdf/math/0209179. pdfmath/0209179. google scholar
- G. Cerda-Morales, 2017, On a Generalization for Tribonacci Quaternions, Mediterranean Journal of Mathematics, 14(239), 1-12. google scholar
- F. T. Howard 2001, A Tribonacci Identity, The Fibonacci Quarterly, 39(4), 352-357. google scholar
- P. Y. Lin,1988, De Moivre-Type Identities For The Tribonacci Numbers,The Fibonacci Quarterly, 26, 131—134. google scholar
- W. Watkins,1987,Generating Function, The College Mathematics Journal, 18(3), 195-211. google scholar
- S. Pethe,1988, Some Identities for Tribonacci sequences, The Fibonacci Quarterly, 26(2), 144—151. google scholar
- Y. Soykan, 2019, Tribonacci and Tribonacci-Lucas Sedenions,Mathematics, 7(1), 2019), 74. arXiv:1808.09248v2. google scholar
- C. C. Yalavigi,1972, Properties of Tribonacci numbers, The Fibonacci Quarterly, 10(3), 231-246. google scholar
- A. G. Shannon and A. F. Horadam,1972, Some Properties of Third-Order Recurrence Relations, The Fibonacci Quarterly, 10(2), 135-145. google scholar
- F. T. Howard and C. Cooper,1970, Some Identities for r-Fibonacci numbers, The Fibonacci Quarterly, 49(3), 231-242. google scholar
- M. E. Waddill and L. Sacks,1967, Another Generalized Fibonacci Sequence, The Fibonacci Quarterly, 59(3), 209-222. google scholar
- T. Komatsu and R. Li, 2017, Convolution identities for Tribonacci numbers with symmetric formulae, 5 Jan 2017, arXiv:1610.02559v2 [math.NT]. google scholar
- Y. Soykan, I. Okumus and E. T. Taşdemir, 2020, On Genralized Tribonacci sedenions, Sarajevo Journal of Mathematics,16(29), 103-122. google scholar
- A. Scott, T. Delaney, V. Jr, Hoggatt 1997, The Tribonacci sequence, The Fibonacci Quarterly, 15(3),193-200. google scholar
- F. T. Howard, 1999, Generalizations of a Fibonacci Identity and parabolic equations, In Applications of Fibonacci Numbers, (Ed. G. E. Bergum et al. Dordrecht), Kluwer, 8 201-211. google scholar
- T. Koshy, 2001, Fibonacci and Lucas Numbers with Applications. In Applications of Fibonacci Numbers, Wiley, New York. google scholar
- N. J. A. Sloane, 1973, A Handbook of Integer Sequences, Academic Press, New York, google scholar
Yıl 2024,
Cilt: 2 Sayı: 2, 87 - 94, 31.12.2024
Öz
This paper presents a generalization of the sequence defined by the third-order recurrence relation𝑉𝑛 (𝑎 𝑗 , 𝑝 𝑗) = Í 3 𝑗=1 𝑝 𝑗𝑉𝑛− 𝑗 , 𝑛 ≥ 4,, 𝑝3 ≠ 0 with initial terms 𝑉𝑗 = 𝑎 𝑗 , where 𝑎 𝑗 and 𝑝 𝑗 𝑗 = 1, 2, 3, are any non-zero real numbers. The generating function and Binet’s formula are derived for this generalized tribonacci sequence. Classical second-order generalized Fibonacci sequences and other existing sequences based on second-order recurrence relations are implicitly included in this analysis. These derived sequences are discussed as special cases of the generalization. A pictorial representation is provided, illustrating the growth and variation of tribonacci numbers for different initial terms 𝑎 𝑗 and coefficients 𝑝 𝑗 . Additionally, the tribonacci constant is examined and visually represented. It is observed that the constant is influenced solely by the coefficients 𝑝 𝑗 of the recurrence relation and is unaffected by the initial terms 𝑎 𝑗 .
Anahtar Kelimeler
Generalized Tribonacci sequence generating function Binet’s formula Tribonacci constan
Kaynakça
- W. R. Spickerman, 1982, Binet’s formula for the Tribonacci Sequence, The Fibonacci Quarterly, 10, 118-120. google scholar
- T. Komatsu, 2018, Convolution Identities for Tribonacci Numbers, Ars Combinatoria, CXXXVI, 199-210. google scholar
- R.Frontczak, 2018, Convolutions for Generalized Tribonacci Numbers and Related Results, International Journal of Mathematical Analysis, 12(7), 307-324. google scholar
- A. G. Shannon,1972, Iterative Formulas Associated with Generalized Third-Order Recurrence Relations. SIM J. Appl. Math., 23(3), 364-367. google scholar
- M. Feinberg, 1963, Iterative Formulas Associated with Generalized Third-Order Recurrence Relations. The Fibonacci Quarterly, 1(1), 71-74. google scholar
- M. Elia, 2001, Derived Sequences, The Tribonacci Recurrence and Cubic Forms. The Fibonacci Quarterly,39(2), 107-109. google scholar
- A. C. F. Bueno, 2015, Notes on Number Theory and Discrete Mathematics,The Fibonacci Quarterly, 21, 67-69. google scholar
- M. Catalani, 2002, Identities for Tribonacci-related sequences, Combinatorics, Available from: https://arxiv.org/pdf/math/0209179. pdfmath/0209179. google scholar
- G. Cerda-Morales, 2017, On a Generalization for Tribonacci Quaternions, Mediterranean Journal of Mathematics, 14(239), 1-12. google scholar
- F. T. Howard 2001, A Tribonacci Identity, The Fibonacci Quarterly, 39(4), 352-357. google scholar
- P. Y. Lin,1988, De Moivre-Type Identities For The Tribonacci Numbers,The Fibonacci Quarterly, 26, 131—134. google scholar
- W. Watkins,1987,Generating Function, The College Mathematics Journal, 18(3), 195-211. google scholar
- S. Pethe,1988, Some Identities for Tribonacci sequences, The Fibonacci Quarterly, 26(2), 144—151. google scholar
- Y. Soykan, 2019, Tribonacci and Tribonacci-Lucas Sedenions,Mathematics, 7(1), 2019), 74. arXiv:1808.09248v2. google scholar
- C. C. Yalavigi,1972, Properties of Tribonacci numbers, The Fibonacci Quarterly, 10(3), 231-246. google scholar
- A. G. Shannon and A. F. Horadam,1972, Some Properties of Third-Order Recurrence Relations, The Fibonacci Quarterly, 10(2), 135-145. google scholar
- F. T. Howard and C. Cooper,1970, Some Identities for r-Fibonacci numbers, The Fibonacci Quarterly, 49(3), 231-242. google scholar
- M. E. Waddill and L. Sacks,1967, Another Generalized Fibonacci Sequence, The Fibonacci Quarterly, 59(3), 209-222. google scholar
- T. Komatsu and R. Li, 2017, Convolution identities for Tribonacci numbers with symmetric formulae, 5 Jan 2017, arXiv:1610.02559v2 [math.NT]. google scholar
- Y. Soykan, I. Okumus and E. T. Taşdemir, 2020, On Genralized Tribonacci sedenions, Sarajevo Journal of Mathematics,16(29), 103-122. google scholar
- A. Scott, T. Delaney, V. Jr, Hoggatt 1997, The Tribonacci sequence, The Fibonacci Quarterly, 15(3),193-200. google scholar
- F. T. Howard, 1999, Generalizations of a Fibonacci Identity and parabolic equations, In Applications of Fibonacci Numbers, (Ed. G. E. Bergum et al. Dordrecht), Kluwer, 8 201-211. google scholar
- T. Koshy, 2001, Fibonacci and Lucas Numbers with Applications. In Applications of Fibonacci Numbers, Wiley, New York. google scholar
- N. J. A. Sloane, 1973, A Handbook of Integer Sequences, Academic Press, New York, google scholar
Toplam 24 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Temel Matematik (Diğer) |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2024 |
| Gönderilme Tarihi | 8 Temmuz 2024 |
| Kabul Tarihi | 24 Aralık 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 2 Sayı: 2 |
