### GENERALIZATION OF PELL SEQUENCE AND PELL-LUCAS SEQUENCE, NEW RESULTS AND CIRCULANT MATRICES ASPECTS

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#### Abstract

Some generalizations of Pell sequence and Pell-Lucas sequence, namely, (k,h)-Pell sequence and (k,h)-Pell-Lucas sequence are considered in this paper. We obtain generating functions, some identities and formulas for the sums of a finite number of terms and consecutive terms, sums of squares of consecutive terms and alternating sums of consecutive terms of these sequences. Then, we obtain the eigenvalues and determinants of particular circulant matrices involving (k,h)-Pell sequence and (k,h)-Pell-Lucas sequence. Finally, we obtain some upper and lower bounds for the spectral norms of these circulant matrices.

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A. C. F. Bueno : Right circulant matrices with Fibonacci sequence . IJMSC . 2 (2012), 8–9.

A. C. F. Bueno : On arithmetic right circulant matrix sequences . IJMSC . 4 1 (2014), 25–27.

A. C. F. Bueno : On the eigenvalues and the determinant of the right circulant matrices with Pell and Pell-Lucas numbers . IJMSC . 4 (1) (2014), 19–20.

D. Bozkurt: A note on the spectral norms of the matrices connected integer numbers sequence . Math. GM . 1 (2011), 171–190.

G. Cerda Morales: Matrix representations of the q-Jacobsthal numbers. Proyecciones (Antofagasta, Online) . 31 4 (2013), 345–354.

Z. Cerin and G. M. Gianella: On sums of Pell numbers . Acc. Sc. Torino – Atti Sc. Fis . (2006), 1–9.

H. Civciv and R. Turkmen: On the bounds for the spectral and ℓp norms of the Khatri-Rao products of Cauchy-Hankel matrices . Jipam . 7 (2006), 365–380.

A. Dasdemir : On the Pell, Pell-Lucas and modified Pell numbers by matrix method. Applied Mathematical Sciences . 5 (64) (2011), 313–318.

E. Dupree and B. Mathes: Singular values of k-Fibonacci and k-Lucas Hankel matrix. Int. J. Contemp. Math. Science. . 7 (2012), 2327–2339.

A. D. Godase and M. B. Dhakne: On the properties of generalized multiplicative coupled fibonacci sequence of rth order. Int. J. Adv. Appl. Math. and Mech . 2 (3) (2015), 252–257.

A. Nali and M. Sen: On the norms of circulant matrices with generalized Fibonacci numbers. Sel¸cuk J. Appl. Math. 1 (2010), 107–116.

S. H. J. Petroudi and M. Pirouz: On some properties of (k,h)-Pell sequence and (k,h)-Pell-Lucass sequence. Int. J. Adv. Appl. Math. and Mech . 3 (1) (2015), 98–101.

S. H. J. Petroudi, M. Pirouz and A. Ozkoc: On Some properties of particular Tetranacci sequence. Int. J. Math. Virtual. (2020), 361–376.

D. T. P. Pili and B. Chathely: A study on circulant matrices and its application in solving polynomial equations and data smoothing. IJMTT. 66 (6) (2020), 275-283.

S. Solak and M. Bahsi: A particular matrix and its some properties. Sci. Res. Essays . 8 (1) (2013), 1–5.

S. Solak and M. Bahsi: On the spectral norms of Toeplitz matrices with Fibonacci and Lucas numbers. Hacet J Math Stat . 42 (1) (2013), 15–19.

O. Talo and Y. Sever: Ideal convergence of double sequence of closed sets. Facta universitis , Ser. Math. Inform. 36 (3) (2021), 605–617.

S. Uygun: Some sum formulas of (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas matrix sequences. Appl. Math, . 92 (2016), 61–69.

DOI: https://doi.org/10.22190/FUMI230717031J

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