Solution of the Rational Difference Equation xn+1=xn−131+xn−1xn−3xn−5xn−7xn−9xn−11{x_{n + 1}} = {{{x_{n - 13}}} \over {1 + {x_{n - 1}}{x_{n - 3}}{x_{n - 5}}{x_{n - 7}}{x_{n - 9}}{x_{n - 11}}}}

[1]Amleh A. M., Grove E. A., Georgiou D. A., (1999), On the recursive sequence xn+1=α+xn−1xn{x_{n + 1}} = \alpha + {{{x_{n - 1}}} \over {{x_n}}} , J. Math. Anal. Appl.AmlehA. M.GroveE. A.GeorgiouD. A.1999On the recursive sequence xn+1=α+xn−1xn{x_{n + 1}} = \alpha + {{{x_{n - 1}}} \over {{x_n}}}J. Math. Anal. Appl.10.1006/jmaa.1999.6346Search in Google Scholar

[2]Amleh A. M., Kirk, V., Ladas G., (2001), On the dynamics of A+α+bxn−1A+Bxn−2A + {{\alpha + {bx_{n - 1}}} \over {A + {Bx_{n - 2}}}} , Math Sci. Res. Hot-Line.AmlehA. M.KirkV.LadasG.2001On the dynamics of A+α+bxn−1A+Bxn−2A + {{\alpha + {bx_{n - 1}}} \over {A + {Bx_{n - 2}}}}Math Sci. Res. Hot-Line.Search in Google Scholar

[3]Cinar C., (2004), On the positive solutions of the difference equation xn+1=xn−11+αxnxn−1{x_{n + 1}} = {{{x_{n - 1}}} \over {1 + \alpha {x_n}{x_{n - 1}}}} , J. Appl. Math.Comput.CinarC.2004On the positive solutions of the difference equation xn+1=xn−11+αxnxn−1{x_{n + 1}} = {{{x_{n - 1}}} \over {1 + \alpha {x_n}{x_{n - 1}}}}J. Appl. Math.Comput.10.1016/S0096-3003(03)00194-2Search in Google Scholar

[4]Cinar C., (2004), On the positive solutions of the difference equation xn+1=xn−1−1αxnxn−1{x_{n + 1}} = {{{x_{n - 1}}} \over { - 1\alpha {x_n}{x_{n - 1}}}} , Appl. Math. Comput.CinarC.2004On the positive solutions of the difference equation xn+1=xn−1−1αxnxn−1{x_{n + 1}} = {{{x_{n - 1}}} \over { - 1\alpha {x_n}{x_{n - 1}}}}Appl. Math. Comput10.1016/S0096-3003(03)00194-2Search in Google Scholar

[5]Cinar C., (2004), On the positive solutions of the difference equation xn+1=αxn−11+bxnxn−1{x_{n + 1}} = {{\alpha {x_{n - 1}}} \over {1 + {bx_n}{x_{n - 1}}}} , Appl. Math. Comput.CinarC.2004On the positive solutions of the difference equation xn+1=αxn−11+bxnxn−1{x_{n + 1}} = {{\alpha {x_{n - 1}}} \over {1 + {bx_n}{x_{n - 1}}}}Appl. Math. Comput.Search in Google Scholar

[6]DeVault R., Ladas G. and Schultz S. W., (1998), On the recursive sequence xn+1=Axn+1xn−2{x_{n + 1}} = {A \over {{x_n}}} + {1 \over {{x_{n - 2}}}} , Proc. Amer. Math. Soc. 24 Dagistan Simsek, Burak Ogul and Fahreddin Abdullayev. Applied Mathematics and Nonlinear Sciences 1(2015) 15–24DeVaultR.LadasG.SchultzS. W.1998On the recursive sequence xn+1=Axn+1xn−2{x_{n + 1}} = {A \over {{x_n}}} + {1 \over {{x_{n - 2}}}}Proc. Amer. Math. Soc.24 Dagistan Simsek, Burak Ogul and Fahreddin Abdullayev. Applied Mathematics and Nonlinear Sciences 1(2015) 15–24Search in Google Scholar

[7]El-Owaidy, H. M., Ahmed, A. M., Mousa, M. S., (2003), On the recursive sequences xn+1=αxn−1β±xn{x_{n + 1}} = {{\alpha {x_{n - 1}}} \over {\beta \pm {x_n}}} , J. Appl. Math. Comput., 145, 747–753.El-OwaidyH. M.AhmedA. M.MousaM. S.2003On the recursive sequences xn+1=αxn−1β±xn{x_{n + 1}} = {{\alpha {x_{n - 1}}} \over {\beta \pm {x_n}}}J. Appl. Math. Comput.14574775310.1016/S0096-3003(03)00271-6Search in Google Scholar

[8]El-Owaidy, H. M., Ahmed, A. M., Elsady, Z., (2004), Global attractivity of the recursive sequences xn+1=α−βxn−1γ+xn{x_{n + 1}} = {{\alpha - \beta {x_{n - 1}}} \over {\gamma + {x_n}}} , J. Appl. Math. Comput., Vol:151, 827–833.El-OwaidyH. M.AhmedA. M.ElsadyZ.2004Global attractivity of the recursive sequences xn+1=α−βxn−1γ+xn{x_{n + 1}} = {{\alpha - \beta {x_{n - 1}}} \over {\gamma + {x_n}}}J. Appl. Math. Comput.15182783310.1016/S0096-3003(03)00539-3Search in Google Scholar

[9]Elabbasy E. M., El-Metwally H., Elsayed E. M., (2006), On the difference equation xn+1=αxn−bxncxn−dxn−1{x_{n + 1}} = \alpha {x_n} - {{{bx_n}} \over {c{x_n} - {dx_{n - 1}}}} , Advances in Difference Equation, 1–10.ElabbasyE. M.El-MetwallyH.ElsayedE. M.2006On the difference equation xn+1=αxn−bxncxn−dxn−1{x_{n + 1}} = \alpha {x_n} - {{{bx_n}} \over {c{x_n} - {dx_{n - 1}}}}Advances in Difference Equation11010.1155/ADE/2006/82579Search in Google Scholar

[10]Elabbasy E. M., El-Metwally H., Elsayed E. M., (2007), On the difference equation xn+1=αxn−kβ+γ∏i=0kxn−i{x_{n + 1}} = {{\alpha {x_{n - k}}} \over {\beta + \gamma \prod\nolimits_{i = 0}^k {x_{n - i}}}} , J. Conc. Appl. Math., 5(2), 101–113.ElabbasyE. M.El-MetwallyH.ElsayedE. M.2007On the difference equation xn+1=αxn−kβ+γ∏i=0kxn−i{x_{n + 1}} = {{\alpha {x_{n - k}}} \over {\beta + \gamma \prod\nolimits_{i = 0}^k {x_{n - i}}}}J. Conc. Appl. Math.52101113Search in Google Scholar

[11]Elabbasy E. M., El-Metwally H., Elsayed E. M., (2007), Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33(4), 861–873.ElabbasyE. M.El-MetwallyH.ElsayedE. M.2007Qualitative behavior of higher order difference equationSoochow Journal of Mathematics334861873Search in Google Scholar

[12]Elabbasy E. M., El-Metwally H., Elsayed E. M., (2007), Global attractivity and periodic character of a fractional difference equation of order three, Yokohama Mathematical Journal, 53, 89–100.ElabbasyE. M.El-MetwallyH.ElsayedE. M.2007Global attractivity and periodic character of a fractional difference equation of order threeYokohama Mathematical Journal5389100Search in Google Scholar

[13]Elabbasy E. M. and Elsayed E. M., (2008), Global attractivity of difference equation of higher order, Carpathian Journal of Mathematics, 24(2), 45–53.ElabbasyE. M.ElsayedE. M.2008Global attractivity of difference equation of higher orderCarpathian Journal of Mathematics2424553Search in Google Scholar

[14]Elaydi, S., (1996), An Introduction to Difference Equations, Spinger-Verlag, New York.ElaydiS.1996An Introduction to Difference EquationsSpinger-VerlagNew York10.1007/978-1-4757-9168-6Search in Google Scholar

[15]Elsayed E. M., (2008), On the solution of recursive sequence of order two, Fasciculi Mathematici, 40, 5–13.ElsayedE. M.2008On the solution of recursive sequence of order twoFasciculi Mathematici40513Search in Google Scholar

[16]Elsayed E. M., (2009), Dynamics of a rational recursive sequences, International Journal of Difference Equations, 4(2), 185–200.ElsayedE. M.2009Dynamics of a rational recursive sequencesInternational Journal of Difference Equations42185200Search in Google Scholar

[17]Elsayed E. M., (2009), Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16(2), 37–50.ElsayedE. M.2009Dynamics of a Recursive Sequence of Higher OrderCommunications on Applied Nonlinear Analysis1623750Search in Google Scholar

[18]Elsayed E. M., (2011), Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, 17–30.ElsayedE. M.2011Solution and atractivity for a rational recursive sequenceDiscrete Dynamics in Nature and Society173010.1155/2011/982309Search in Google Scholar

[19]Elsayed E. M., (2011), On the solution of some difference equation, Europan Journal of Pure and Applied Mathematics, 4(3), 287–303.ElsayedE. M.2011On the solution of some difference equationEuropan Journal of Pure and Applied Mathematics43287303Search in Google Scholar

[20]Elsayed E. M., (2012), On the Dynamics of a higher order rational recursive sequence, Communications in Mathematical Analysis, 12(1), 117–133.ElsayedE. M.2012On the Dynamics of a higher order rational recursive sequenceCommunications in Mathematical Analysis12111713310.1186/1687-1847-2012-69Search in Google Scholar

[21]Elsayed E. M., (2012), Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, 378–384.ElsayedE. M.2012Solution of rational difference system of order twoMathematical and Computer Modelling5537838410.1016/j.mcm.2011.08.012Search in Google Scholar

[22]Elsayed E. M., (2016), Dynamics of a three-dimensional systems of rational difference equations, Mathematical Methods in the Applied Sciences, 39(5), 1026–1038.ElsayedE. M.2016Dynamics of a three-dimensional systems of rational difference equationsMathematical Methods in the Applied Sciences3951026103810.1002/mma.3540Search in Google Scholar

[23]Elsayed E. M., (2016), Dynamics of behavior of a higher order rational difference equation, The Journal of Nonlinear Science and Applications, 9(4), 1463–1474.ElsayedE. M.2016Dynamics of behavior of a higher order rational difference equationThe Journal of Nonlinear Science and Applications941463147410.22436/jnsa.009.04.06Search in Google Scholar

[24]Elsayed E. M., (2015), New method to obtain periodic solutions of period two and three of a rational difference equation, Nonlinear Dynamics, 79(1), 241–250.ElsayedE. M.2015New method to obtain periodic solutions of period two and three of a rational difference equationNonlinear Dynamics79124125010.1007/s11071-014-1660-2Search in Google Scholar

[25]Simsek D., Cinar C., Yalcinkaya I., (2006), On the recursive sequence xn+1=xn−31+xn−1{x_{n + 1}} = {{{x_{n - 3}}} \over {1 + {x_{n - 1}}}} , Internat. J. Contemp. 9(12), 475–480.SimsekD.CinarC.YalcinkayaI.2006On the recursive sequence xn+1=xn−31+xn−1{x_{n + 1}} = {{{x_{n - 3}}} \over {1 + {x_{n - 1}}}}Internat. J. Contemp.912475480Search in Google Scholar

[26]Simsek D., Cinar C., Karatas R., Yalcinkaya I., (2006), On the recursive sequence xn+1=xn−51+xn−2{x_{n + 1}} = {{{x_{n - 5}}} \over {1 + {x_{n - 2}}}} , Int. J. Pure Appl. Math., 27(4), 501–507.SimsekD.CinarC.KaratasR.YalcinkayaI.2006On the recursive sequence xn+1=xn−51+xn−2{x_{n + 1}} = {{{x_{n - 5}}} \over {1 + {x_{n - 2}}}}Int. J. Pure Appl. Math.274501507Search in Google Scholar

[27]Simsek D., Cinar C., Karatas R., Yalcinkaya I., (2006), On the recursive sequence xn+1=xn−51+xn−1xn−3{x_{n + 1}} = {{{x_{n - 5}}} \over {1 + {x_{n - 1}}{x_{n - 3}}}} , Int. J. Pure Appl. Math., 28(1), 117–124.SimsekD.CinarC.KaratasR.YalcinkayaI.2006On the recursive sequence xn+1=xn−51+xn−1xn−3{x_{n + 1}} = {{{x_{n - 5}}} \over {1 + {x_{n - 1}}{x_{n - 3}}}}Int. J. Pure Appl. Math.281117124Search in Google Scholar

[28]Simsek D., Cinar C., Yalcinkaya I., (2008), On the recursive sequence xn+1=xn−(5k+9)1+xn−4xn−9xn−(5k+4){x_{n + 1}} = {{{x_{n - (5k + 9)}}} \over {1 + {x_{n - 4}}{x_{n - 9}}{x_{n - (5k + 4)}}}} Taiwanese Journal of Mathematics, 12(5), 1087–1098.SimsekD.CinarC.YalcinkayaI.2008On the recursive sequence xn+1=xn−(5k+9)1+xn−4xn−9xn−(5k+4){x_{n + 1}} = {{{x_{n - (5k + 9)}}} \over {1 + {x_{n - 4}}{x_{n - 9}}{x_{n - (5k + 4)}}}}Taiwanese Journal of Mathematics1251087109810.11650/twjm/1500574249Search in Google Scholar

[29]Simsek D., Ogul B., Abdullayev F., (2017), Solutions of the rational difference equations xn+1=xn−111+xn−2xn−5xn−8{x_{n + 1}} = {{{x_{n - 11}}} \over {1 + {x_{n - 2}}{x_{n - 5}}{x_{n - 8}}}} , AIP Conference Proceedings 1880(1) 040003.SimsekD.OgulB.AbdullayevF.2017Solutions of the rational difference equations xn+1=xn−111+xn−2xn−5xn−8{x_{n + 1}} = {{{x_{n - 11}}} \over {1 + {x_{n - 2}}{x_{n - 5}}{x_{n - 8}}}}AIP Conference Proceedings1880104000310.1063/1.5000619Search in Google Scholar

[30]Simsek D., Abdullayev F., (2017), On the Recursive Sequence xn+1=αxn−4k+31+∏t=02xn−(k+1)t−k{x_{n + 1}} = {{\alpha {x_{n - 4k + 3}}} \over {1 + \prod\nolimits_{t = 0}^2 {x_{n - (k + 1)t - k}}}} , Journal of Mathematics Sciences, 222(6), 762–771.SimsekD.AbdullayevF.2017On the Recursive Sequence xn+1=αxn−4k+31+∏t=02xn−(k+1)t−k{x_{n + 1}} = {{\alpha {x_{n - 4k + 3}}} \over {1 + \prod\nolimits_{t = 0}^2 {x_{n - (k + 1)t - k}}}}Journal of Mathematics Sciences222676277110.1007/s10958-017-3330-7Search in Google Scholar

[31]Simsek D., Dogan A., (2014), On A Class of Recursive Sequence, Manas Journal of Engineering, 2(1), 16–22.SimsekD.DoganA.2014On A Class of Recursive SequenceManas Journal of Engineering211622Search in Google Scholar

[32]Simsek D., Ogul B., (2017), Solutions of the Rational Difference Equations xn+1=xn−(2k+1)1+xn−k{x_{n + 1}} = {{{x_{n - (2k + 1)}}} \over {1 + {x_{n - k}}}} , Manas Journal of Engineering, 5(3), 57–68.SimsekD.OgulB.2017Solutions of the Rational Difference Equations xn+1=xn−(2k+1)1+xn−k{x_{n + 1}} = {{{x_{n - (2k + 1)}}} \over {1 + {x_{n - k}}}}Manas Journal of Engineering53576810.1063/1.5000619Search in Google Scholar

[33]Simsek D., Ogul B., (2018), Solutions of the Rational Difference Equations, Manas Journal of Engineering, 6(1), 56–74.SimsekD.OgulB.2018Solutions of the Rational Difference EquationsManas Journal of Engineering615674Search in Google Scholar