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Liczba wyników
2014 | 34 | 1-2 | 63-69

Tytuł artykułu

On useful schema in survival analysis after heart attack

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers

Twórcy

  • Department of Differential Equations and Statistics, Faculty of Mathematics and Natural Sciences, University of Rzeszów, Pigonia 1, 35-959 Rzeszów, Poland

Bibliografia

  • [1] H. Belbachir and A. Benmezai, An alternative approach to Cigler's q-Lucas polynomials, Appl. Math. Computat. 226 (2014) 691-698. doi: 10.1016/j.amc.2013.10.009
  • [2] G.B. Diordjević, Generating functions of the incomplete generalized Fibonacci and generalized Lucas numbers, Fibonacci Quart. 39 (2004) 106-113.
  • [3] A. Dil and I. Mező, A symmetric algorithm for hyperharmonic and Fibonacci numbers, Appl. Math. Comput. 206 (2008) 942-951. doi: 10.1016/j.amc.2008.10.013
  • [4] M. El-Mikkawy and T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456-4461. doi: 10.1016/j.amc.2009.12.069
  • [5] X. Fu and X. Zhou, On matrices related with Fibonacci and Lucas numbers, Appl. Math. Comput. 200 (2008) 96-100. doi: 10.1016/j.amc.2007.10.060
  • [6] D. Garth, D. Mills and P. Mitchell, Polynomials generated by the Fibonacci sequence, J. Integer. Seq. 10 (2007), Article 07.6.8.
  • [7] H.H. Gulec, N. Taskara and K. Uslu, A new approach to generalized Fibonacci and Lucas numbers with binomial coefficients, Appl. Math. Comput. 230 (2013) 482-486. doi: 10.1016/j.amc.2013.05.043
  • [8] J.M. Gutiérrez, M.A. Hernández, P.J. Miana and N. Romero, New identities in the Catalan triangle, J. Math. Anal. Appl. 341 (2008) 52-61. doi: 10.1016/j.jmaa.2007.09.073
  • [9] P. Hao and S. Zhi-wei, A combinatorial identity with application to Catalan numbers, Discrete Math. 306 (2006) 1921-1940. doi: 10.1016/j.disc.2006.03.050
  • [10] V.E. Hoggat Jr., Fibonacci and Lucas Numbers, Houghton Miffin (Boston, MA, 1969).
  • [11] H. Hosoya, Fibonacci triangle, Fibonacci Quart. 14 (1976) 173-178.
  • [12] B.D. Jones, Comprehensive Medical Terminology, Third Ed. Delmar Publishers (Albany NY, 2008).
  • [13] S. Kitaev and J. Liese, Harmonic numbers, Catalan's triangle and mesh patterns, Discrete Math. 313 (2013) 1515-1531. doi: 10.1016/j.disc.2013.03.017
  • [14] E.G. Kocer and N. Touglu, The Binet formulas for the Pell-Lucas p-numbers, Ars Combinatoria 85 (2007) 3-18.
  • [15] T. Koshy, Fibonacci and Lucas Numbers with Applications (Wiley-Interscience, New York, 2001). doi: 10.1002/9781118033067
  • [16] T. Koshy, Fibonacci, Lucas, and Pell numbers, and Pascal's triangle, Math. Spectrum 43 (2011) 125-132.
  • [17] H. Kwong, Two determinants with Fibonacci ad Lucas entries, Appl. Math. Comput. 194 (2007) 568-571. doi: 10.1016/j.amc.2007.04.027
  • [18] S.-M. Ma, Identities involving generalized Fibonacci-type polynomials, Appl. Math. Comput. 217 (2011) 9297-9301. doi: 10.1016/j.amc.2011.04.012
  • [19] L. Niven, H. Zuckerman and H. Montgomery, An Introduction to the Theory of Numbers, Fifth Ed. (Wiley, New York, 1991).
  • [20] J. Petronilho, Generalized Fibonacci sequences via orthogonal polynomials, Appl. Mat. Comput. 218 (2012) 9819-9824. doi: 10.1016/j.amc.2012.03.053
  • [21] L.W. Shapiro, A Catalan triangle, Discrete Math. 14 (1976) 83-90. doi: 10.1016/0012-365X(76)90009-1
  • [22] N. Sloane, On-Line Encyclopedia of Integer Sequences (OEIS), http;//oeis.org.
  • [23] S. Stanimirović, Some identities on Catalan numbers and hypergeometric functions via Catalan matrix power, Appl. Math. Comput. 217 (2011) 9122-9132. doi: 10.1016/j.amc.2011.03.138
  • [24] S. Stanimirović, P. Stanimirović, M. Miladinović and A. Ilić, Catalan matrix and related combinatorial identities, Appl. Math. Comput. 215 (2009) 796-805. doi: 10.1016/j.amc.2009.06.003
  • [25] C. Stępniak, On distribution of waiting time for the first failure followed by a limited length success run, Appl. Math. (Warsaw) (2013) 421-430. doi: 10.4064/am40-4-3
  • [26] N. Tuglu, E.G. Kocer and A. Stakhov, Bivariate fibonacci like p-polynomials, Appl. Math. Comput. 217 (2011) 10239-10246. doi: 10.1016/j.amc.2011.05.022
  • [27] S. Vajda, Fibonacci and Lucas Numbers and the Golden Section, Ellis Horwood (Chichester 1989).
  • [28] N.N. Vorobyov, Fibonacci Numbers, Publishing House 'Nauka', Moscow, 1961 (in Russian).
  • [29] A. Włoch, Some identities for the generalized Fibonacci numbers and the generalized Lucas numbers, Appl. Math. Comput. 219 (2013) 5564-5568. doi: 10.1016/j.amc.2012.11.030
  • [30] O. Yayenie, A note on generalized Fibonacci sequences, Appl. Math. Comput. 217 (2011) 5603-5611. doi: 10.1016/j.amc.2010.12.038

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Bibliografia

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