## Akcije

kako citirati ovaj članak
podeli ovaj članak

## Metrika

• citati u SCIndeksu: 0
• citati u CrossRef-u:0
• posete u poslednjih 30 dana:11
• preuzimanja u poslednjih 30 dana:7

 članak: 4 od 65
 povratak na rezultate
2022, vol. 26, br. 1, str. 77-88
(naslov ne postoji na srpskom)
aKafkas University, Faculty of Science and Letters, Department of Mathematics, Kars, Turkey
bPamukkale University, Faculty of Science and Arts, Department of Mathematics, Denizli, Turkey

Ključne reči: The complex-type Padovan-p sequence; matrix; representation
Sažetak
(ne postoji na srpskom)
In this paper, we define the complex-type Padovan-p sequence and then give the relationships between the Padovan-p numbers and the complex-type Padovan-p numbers. Also, we provide a new Binet formula and a new combinatorial representation of the complex-type Padovan-p numbers by the aid of the nth power of the generating matrix of the complex-type Padovan-p sequence. In addition, we derive various properties of the complex-type Padovan-p numbers such as the permanental, determinantal and exponential representations and the finite sums by matrix methods.
 Reference Berzsenyi, G. (1975) Sums of products of generalized Fibonacci numbers. Fibonacci Quarterly, 13(4): 343-344 Brualdi, R.A., Gibson, P.M. (1977) Convex polyhedra of doubly stochastic matrices I: Applications of permanent function. Journal of Combinatorial Theory, Series A, 22(2): 194-230 Chen, W.Y.C., Louck, J.D. (1996) The combinatorial power of the companion matrix. Linear Algebra and its Applications, 232: 261-278 Deveci, O., Karaduman, E. (2017) On The Padovan p-numbers. Hacettepe Journal of Mathematics and Statistics, 2(46): 579-592 Deveci, Ö., Shannon, A.G. (2021) The complex-type k-Fibonacci sequences and their applications. Communications in Algebra, 49(3): 1352-1367 Deveci, Ö., Shannon, A.G. (2018) The quaternion-Pell sequence. Communications in Algebra, 46(12): 5403-5409 Horadam, A.F. (1961) A generalized Fibonacci sequence. American Mathematical Monthly, 68(5): 455-459 Horadam, A.F. (1963) Complex Fibonacci numbers and Fibonacci quaternions. American Mathematical Monthly, 70(3): 289-291 Horadam, A.F., Shannon, A.G. (1976) Ward's Staut-Clausen problem. Mathematica Scandinavica, 39(2): 239-250 Kalman, D. (1982) Generalized Fibonacci numbers by matrix methods. Fibonacci Quarterly, 20 (1): 73-76 Kilic, E. (2008) The Binet formula, sums and representations of generalized Fibonacci p-numbers. European Journal of Combinatorics, 29(3): 701-711 Kilic, E., Taşci, D. (2007) On The permanents of some tridiagonal matrices with applications to The Fibonacci and Lucas numbers. Rocky Mountain Journal of Mathematics, 37(6): 1953-1969 Kiliç, E., Taşci, D. (2006) On The generalized order-$k$ Fibonacci and Lucas numbers. Rocky Mountain Journal of Mathematics, 36(6): 1915-1926 Lancaster, P., Tismenetsky, M. (1985) The theory of matrices: With applications. Elsevier Lidl, R., Niederreiter, H. (1994) Introduction to finite fields and their applications. Cambridge University Press Ozgur, N.Y. (2005) On The sequences related to Fibonacci and Lucas numbers. Journal of the Korean Mathematical Society, 42(1): 135-151 Shannon, A.G. (1974) Explicit expressions for powers of arbitrary order linear recursive sequences. Fibonacci Quarterly, 12(3): 281-287 Shannon, A.G. (1974) Some properties of a fundamental recursive sequence of arbitrary order. Fibonacci Quarterly, 12(4): 327-335 Shannon, A.G. (1976) Ordered partitions and arbitrary order linear recurrence relations. Mathematics Student, 43 (3): 110-117 Stakhov, A.P., Rozin, B. (2006) Theory of Binet formulas for Fibonacci and Lucas p-numbers. Chaos, Solitons & Fractals, 27(5): 1162-1177 Stakhov, A.P., Rozin, B. (2006) The continuous functions for the Fibonacci and Lucas p-numbers. Chaos, Solitons & Fractals, 28(4): 1014-1025 Tasci, D., Firengiz, M.C. (2010) Incomplete Fibonacci and Lucas p-numbers. Mathematical and Computer Modelling, 52: 1763-1770