[1] H. Belbachir, T. Komatsu and L. Szalay, Characterization of linear recurrences asso¬ciated to rays in Pascal's triangle, AIP Conf. Proc. 1264 (2010), 90-99; Diophantine analysis and related fields 2000, Amer. Math. Phys., Melville, NY, 2010.
[2] H. Belbachir, T. Komatsu and L. Szalay, Linear recurrences associated to rays in Pascal's triangle and combinatorial identities, Math. Slovaca, 64(2) (2014), 287-300..
[3] N.H. Bong, Fibonacci matrices and matrix representation of Fibonacci numbers,
Southeast Asian Bull. Math., 23 (1999), 357-374.
[4] C. K. Cook and T. Komatsu, Some identities for sequences ob binomial sums of generalized Fibonacci numbers, The Fibonacci Quarterly, 54(2) (2016), 105-111.
[5] P. Haukkanen, Binomial formulas for specially multiplicative functions, Math. Stu¬dent 64(1-4) (1995), 155-161.
[6] V.E. Hoggat, Jr and M. Bicknell-Johnson, A matrix representation of Fibonacci iden¬tities for F2nk, A collection of Manuscripts related to the Fibonacci sequence, 18th Anniversary Volume, pp. 114-124, The Fibonacci Association, 1980.
[7] E. Kılıç and P.Stanica, Factorizations and representations of second order linear recur¬rences with indices in arithmetic progressions, Bulletin of the Mexican Mathematical
Society 15(1) (2009), 23-36.
[8] E. Kılıç, N. Ömür and Y. Türker Ulutas, Matrix representation of the second order recurrence {ukn} , Ars combinatoria, 93 (2009), 181-190.
[9] E.
Kılıcç
, I. Akkuçs, N. Öümuür and Y. Tuürker Ulutaçs, A curious matrix-sum identity and certain finite sums identities, Asian-European Journal of Mathematics, 8(3) (2015),
1550047-1-10.
REFERENCES
515
[10] J. Mc Laughlin, Combinatorial identities deriving from the nth power of a 2 x 2 matrix, Integers, 4 (2004) A19, 15pp.
[11] T. Komatsu, Some generalized Fibonacci identitis including powers and binomial coefficients, The Fibonacci Quarterly, 52(1) (2014), 50-60.
[12] T. Koshy, Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience
Publications, New York, 2001.
[13] J. Mc Laughlin, Combinatorial identities deriving from the nth power of a 2 x 2 matrix, Integers, 4 (2004) A19, 15pp.
[14] J. Mc Laughlin and N. J. Wyshinski, Further combinatorial identities deriving from the nth power of a 2 x 2 matrix, Discrete Applied Mathematics, 154(8) (2006), 1301¬1308.
[15] M.E. Waddill, Matrices and generalized Fibonacci sequences, Fibonacci Quart.12
(1974), 381-386.
[16] K.S. Williams, The nth power of a 2 x 2 matrix, Math. Mag. 65(5) (1992), 336.
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