PUBLICATIONS

 

1. D. Taşcı and E. Kılıç, On the order-k generalized Lucas numbers, Applied Mathematics Computation 155 (3) (2004), 637–641.

 

2. E. Kılıç and D. Taşcı, On the generalized order-k Fibonacci and Lucas numbers, Rocky Mountain Journal of Mathematics 36 (6) (2006), 1915–1926.

 

3. E. Kılıç and D. Taşcı, The linear algebra of the Pell matrix, Bulletin of the Mexican Mathematical Society 2 (11) (2005), 163–174.

 

4. E. Kılıç, B. Altunkaynak and D. Taşcı, On the computing of the generalized order-k Pell numbers in log time, Applied Mathematics Computation 181 (1) (2006), 511–515.

 

5. E. Kılıç and D. Taşcı, The generalized Binet formula, representation and sums of the generalized order-k Pell numbers, Taiwanese J. Math. 10 (6) (2006), 1661–1670.

 

6. E. Kılıç and D. Taşcı, Factorizations and representations of the backward second order linear recurrences, J. Comput. Appl. Math. 201 (1) (2007), 182–197.

 

7. E. Kılıç, The generalized order-k Fibonacci-Pell sequence by matrix methods, J. Comput. Appl. Math. 209 (2) (2007), 133–145.

 

8. E. Kılıç, Sums of generalized Fibonacci numbers by matrix methods, Ars Combinatoria, 84 (2007), 23–31.

 

9. E. Kılıç and D. Taşcı, On the permanents of some tridiagonal matrices with applications to the Fibonacci and Lucas numbers, Rocky Mountain Journal of Mathematics 37 (6) (2007), 203–219.

 

10. E. Kılıç and D. Taşcı, On sums of second order linear recurrences by hessenberg matrices, Rocky Mountain Journal of Mathematics 38 (2) (2008), 531–544.

 

11. E. Kılıç, Sums of the squares of terms of sequence {un}, Proc. Indian Acad. Sci. 118 (1) (2008), 27–41.

 

12. E. Kılıç, The Binet formula, sum and representations of generalized Fibonacci p-numbers, European Journal of Combinatorics 29 (3) (2008), 701–711.

 

13. E. Kılıç, Explicit formula for the inverse of a tridiagonal matrix by backward continued fractions, Applied Mathematics Computation 197 (1) (2008), 345–357.

 

14. E. Kılıç, Formulas for sums of generalized order-k Fibonacci type, Ars Combinatoria 86 (2008), 395–402.

 

15. E. Kılıç, Tribonacci sequences with certain indices and their sums, Ars Combinatoria 86 (2008), 13–22.

 

16. E. Kılıç and M. El-Mikkawy, A computational algorithm for special nth order pentadiagonal Toeplitz determinants, Applied Mathematics Computation 199 (2) (2008), 820–822.

 

17. E. Kılıç, On a constant-diagonals matrix, Applied Mathematics Computation  204 (1) (2008), 184–190.

 

18. E. Kılıç and D. Tasci, Generalized order-k Fibonacci and Lucas functions, Rocky Mountain Journal of Mathematics 38 (6) (2008), 1991–2007.

 

19. E. Kılıç and N. Irmak, Reciprocal sums of l-th power of generalized binary sequences with indices, Ars Combintoria 88 (2008), 407–413.

 

20. E. Kılıç, On the usual Fibonacci and generalized order-k Pell numbers, Ars Combinatoria 88 (2008), 33–45.

 

21. E. Kılıç, G. N. Stanica and P. Stanica, Spectral properties of some combinatorial matrices, Congressus Numerantium Vol. 201, Proc. International Conf. Fibonacci Numbers & Applications (2010), 223–236.

 

22. E. Kılıç and D. Tasci, On families of bipartite graphs associated with sums of Fibonacci and Lucas numbers, Ars Combinatoria 89 (2008), 31–40.

 

23. E. Kılıç and P. Stanica, Generating matrices for weighted sums of a second order linear recurrence, Journal of Integer Sequences 12 (2009) Article 09.2.7.

 

24. E. Kılıç, On the second order linear recurrences by tridiagonal matrices, Ars Combinatoria 91 (2009), 11–18.

 

25. E. Kılıç, The generalized Pell (p,i)- numbers and their Binet formulas, combinatorial representations, sums, Chaos, Solitons and Fractals 40 (2009), 2047–2063.

 

26. E. Kılıç and A.P. Stakhov, On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices, Chaos, Solitons and Fractals 40 (2009), 2210–2221.

 

27. E. Kılıç, N. Ömür, G. Tatar and Y. Ulutaş, Factorizations of the Pascal matrix via generalized second order recurrent matrix, Hacettepe Journal of Mathematics and Statistics 38 (3) (2009), 305–316.

 

28. E. Kılıç and D. Taşcı, On the second order linear recurrence satisfied by the permanent of generalized doubly stochastic matrices, Ars Combinatoria 93 (2009), 1–14.

 

29. E. Kılıç, N. Ömür and Y. Ulutaş, Matrix representations for the second order recurrence {Ukn}, Ars Combinotaria 93 (2009), 181–190.

 

30. E. Kılıç, More general identities involving the terms of {Wn(a,b;p,q)}, Ars Combinatoria 93 (2009), 459–461.

 

31. E. Kılıç and P. Stanica, Factorizations and representations of second order linear recurrences with indices in arithmetic progressions, Bulletin of the Mexican Mathematical Society 15 (1) (2009), 23–36.

 

32. E. Kılıç, The generalized Fibonomial matrix, European Journal of Combinatorics 31 (2010), 193–209.

 

33. E. Kılıç and D. Taşcı, On the generalized Fibonacci and Pell sequences by hessenberg matrices, Ars Combinatoria 94 (2010), 161–174.

 

34. E. Kılıç and D. Taşcı, On families of bipartite graphs associated with sums of generalized order-k Fibonacci and Lucas numbers, Ars Combinatoria 94 (2010), 13–23.

 

35. E. Kılıç and N. Ömür, Conics characterizing the generalized Fibonacci and Lucas sequences with indices in arithmetic progressions, Ars Combinatoria 94 (2010), 459–464.

 

36. E. Kılıç and H. Prodinger, A generalized Filbert matrix, The Fibonacci Quarterly, 48 (1) (2010), 29–33.

 

37. E. Kılıç, D. Taşcı and P. Haukkanen, On the generalized Lucas sequences by hessenberg matrices, Ars Combinatoria 95 (2010), 383–395.

 

38. E. Kılıç and D. Taşcı, Negatively subscripted Fibonacci and Lucas numbers and their complex factorizations, Ars Combinatoria 96 (2010), 275–288.

 

39. E. Kılıç and E. J. Ionascu, Certain binomial sums with recursive coefficients, The Fibonacci Quarterly 48 (2) (2010), 161–167.

 

40. E. Kılıç, İ. Akkuş and H. Prodinger, A proof of a conjecture of Melham, The Fibonacci Quarterly 48 (3) (2010), 241–248.

 

41. E. Kılıç, Second order linear recursions whose subscripts are a power, Miskolc Mathematical Notes 11 (2) (2010), 151–161.

 

42. E. Kılıç and P. Stanica, The Lehmer matrix and its recursive analogue, Journal of Combinatorial Mathematics and Combinatorial Computing 74 (2010), 193–207.

 

43. E. Kılıç, On binomial sums for the general second order linear recurrence, Integers: The Electronic Journal of Combinatorial Number Theory #A57, 10 (2010), 801–806.

 

44. E. Kılıç and P. Stanica, A matrix approach for general higher order linear recurrence, Bulletin of the Malaysian Mathematical Sciences Society (2) 34 (1) (2011), 51–67.

 

45. E. Kılıç and N. Irmak, Binomial identities involving the generalized Fibonacci type polynomials, Ars Combinatoria 98 (2011), 129–134.

 

46. E. Kılıç, N. Ömür and Y. Ulutaş, Binomial sums whose coefficients are products of terms of binary sequences, Utilitas Mathematica 84 (2011), 45–52.

 

47. E. Kılıç, Y. Ulutaş and N. Ömür, Sums of products of the terms of generalized Lucas sequence {Vkn}, Hacettepe Journal of Mathematics and Statistics 40 (2) (2011), 147–161.

 

48. E. Kılıç and P. Stanica, Factorizations and representations of binary polynomial recurrences by matrix methods, Rocky Mountain Journal of Mathematics 41 (4) (2011), 1247–1264.

 

49. E. Kılıç, Y. Ulutaş and N. Ömür, A formula for the generating functions of powers of Horadam's sequence with additional 2 parameters, Journal of Integer Sequences 14 (2011) Article 11.5.6.

 

50. E. Kılıç, N. Ömür and Y. Ulutaş, Alternating sums of the powers of Fibonacci and Lucas numbers, Miskolc Mathematical Notes 12 (1) (2011), 87–103.

 

51. E. Kılıç and P. Stanica, Generating matrices of C-nomial coefficients and their spectra, accepted in Proc. International Conf. Fibonacci Numbers & Applic. 2010.

 

52. E. Kılıç, N. Ömür and Y. Ulutaş, Some finite sums involving generalized Fibonacci and Lucas numbers, Discrete Dynamics in Nature and Society (2011), Article ID 284261.

 

53. E. Kılıç, H. Prodinger, I. Akkuş and H. Ohtsuka, Formulas for Fibonomial sums with generalized Fibonacci and Lucas coefficients, The Fibonacci Quarterly 49 (4) (2011), 320–329.

 

54. E. Kılıç, İ. Akkuş and H. Ohtsuka, Some generalized Fibonomial sums related with the Gaussian q-binomial sums, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie 55 (103) (1) (2012), 51–61.

 

55. E. Kılıç, Y. Ulutaş and N. Ömür, Formulas for weighted binomial sums with the powers of terms of binary recurrences, Miskolc Mathematical Notes 13 (1) (2012), 53–65.

 

56. E. Kılıç, A matrix approach for generalizing two curious divisibility properties, Miskolc Mathematical Notes 13 (2) (2012), 389–396.

 

57. E. Kılıç, N. Ömür and G. Tatar, Riordan group approaches in matrix factorizations, Bulletin of the Iranian Mathematical Society 38 (2) (2012), 491–506.

 

58. E. Kılıç and H. Prodinger, The q-Pilbert matrix, International Journal Computers Mathematics 89 (10) (2012), 1370–1377.

 

59. E. Kılıç and P. Stanica, General approach in computing sums of products of binary sequences, Hacettepe Journal of Mathematics and Statistics 42 (1) (2013), 1–7.

 

60. E. Kılıç and P. Stanica, The inverse of banded matrices, Journal of Computational and Applied Mathematics 237 (1) (2013), 126–135.

 

61. E. Kılıç and T. Arıkan, More on the infinite sum of reciprocal usual Fibonacci, Pell and higher order recurrences, Applied Mathematics Computation 219 (14) 2013, 7783–7788.

 

62. E. Kilic and N. Ömür, Some weighted sums of products of Lucas sequences, Integers: The Electronic Journal of Combinatorial Number Theory 13 (2013), #A27, 1–9.

 

63. E. Kılıç and H. Prodinger, Variants of the Filbert Matrix, The Fibonacci Quarterly 51 (2) (2013), 153–162.

 

64. E. Kılıç and H. Prodinger, Some Double binomial sums related to Fibonacci, Pell and generalized order-k Fibonacci numbers, Rocky Mountain Journal of Mathematics 43 (3) (2013), 975–987.

 

65. E. Kılıç, Sylvester-tridiagonal matrix with alternating main diagonal entries and its spectra, International Journal Nonlinear Sciences and Numerical Simulation 14 (5) (2013), 261–266.

 

66. E. Kılıç and H. Prodinger, Asymmetric generalizations of the Filbert matrix and variantsPublications de'l Institut Mathematique 95 (109) (2014), 267–280.

 

67. E. Kılıç and H. Prodinger, A note on the conjecture of Ramirez and Sirvent, Journal of Integer Sequences 2014, Article 14.5.8.

 

68. E. Kılıç and Aynur Yalçıner, New sums identities in weighted Catalan triangle with the powers of generalized Fibonacci and Lucas numbers, Ars Combinatoria 115 (2014), 391–400.

 

69. E. Kılıç, İ. Akkuş and H. Prodinger, A generalization of a conjecture of MelhamUtilitas Mathematica 93 (2014), 225–232.

 

70. E. Kılıç and H. Prodinger, The generalized q-Pilbert matrixMathematica Slovaca 64 (5) (2014), 1–10.

 

71. E. Kılıç, A proof of a conjecture of Marques and TrojovskyMiskolc Mathematical Notes 2 (2) (2014), 545–557.

 

72. E. Kılıç, Y. Ulutaş, I. Akkuş and N. Ömür, Generalized binary recurrent quasi-cyclic matricesAnnales Mathematicae et Informaticae 43 (2014), 103–112.

 

73. E. Kılıç and H. Prodinger,  Formulae related to the q-Dixon formula with applications to  Fibonomial sums, (short version) Periodica Mathematica Hungarica. (long version) 70 (2015), 216–226.

 

74. E. Kılıç, Some subsequences of the generalized Fibonacci and Lucas numbersUtilitas Mathematica 97 (2015), 233-239.

 

75. E. Kılıç, I. Akkuş,  N. Ömür and Y. Ulutaş, Various sums including the generalized Fibonacci and Lucas numbersPalestine Journal of Mathematics 4 (2) (2015) , 319–326.

 

76. E. Kılıç and H. Prodinger, Sums of products of generalized Fibonacci and Lucas numbersActa Mathematica Hungarica 145 (1) (2015), 17–25.

 

77. E. Kılıç and H. Prodinger, Closed form evaluation of sums containing squares of Fibonomial coefficients, Mathematica Slovaca 66 (3) (2016), 757–765.

 

78. E. Kılıç and Hacene Belbachir, Generalized double binomial sums families by generating functions, acceped in Utilitas Mathematica.

 

79. E. Kılıç, I. Akkuş,  N. Ömür and Y. Ulutaş, Formulas for binomial sums including powers of Fibonacci and Lucas numbersU.P.B. Sci. Bull.,Series A 77 (4) (2015), 69–78.

 

80. E. Kılıç, İ. Akkuş, N. Ömür, Y. Ulutaş, A curious matrix-sum identity and certain finite sums identitiesAsian-European Journal of Mathematics 8 (3) (2015), #1550047.

 

81. E. Kılıç and H. Prodinger, Evaluation of sums involving Gaussian q-binomial coefficients with rational weight functionsInternational Journal of Number Theory 12 (2) (2016), 495–504.

 

82. Emrah Kılıç, İlker Akkuş and Gonca Kızılaslan, A variant of the reciprocal super Catalan matrix with two additional parameters, Spec. Matrices 3 (2015); 163–168.

 

83. E. Kılıç, I. Akkus, N. Ömür, Y. Ulutaş, Generalized binomial convolution of the mth powers of the consecutive integers with the general Fibonacci sequence, Demonstratio Mathematica 49 (4) (2016), 379–385.

 

84. E. Kılıç and T. Arıkan, Evaluation of spectrum of 2-periodic tridiagonal-Sylvester matrix, Turkish Journal of Mathematics 40 (2016), 80–89.

 

85. E. Kılıç and H. Prodinger, The generalized Lilbert matrix, Periodica Mathematica Hungarica 73 (1) (2016), 62–72.

 

86. E. Kılıç and T. Arıkan, The generalized reciprocal super Catalan matrix, Turkish Journal of Mathematics 40 (2016), 960-972.

 

87. E. Kılıç, Some classes of alternating weighted binomial sums, Annals of the Alexandru Ioan Cuza University – Mathematics 3(2) (2016), 835—843.

 

88. E. Kılıç and T. Arıkan, Ruehr's identities with two additional parameters, Integers, 16 (2016), #A30.

 

89. E. Kılıç and H. Prodinger, Some Gaussian binomial sum formulæ with applications, Indian J. Pure Appl. Math. 47 (3) (2016), 399–407.

 

90. E. Kılıç, Neşe Ömür, Sibel Koparal, Yücel Ulutaş, Two variants of the reciprocal super Catalan matrix,  Kyungpook Mathematical Journal 56 (2) (2016), 409–418.

 

91. E. Kılıç and H. Prodinger,  Identities with squares of binomial coefficients: an elementary and explicit approach, Publications de l'Institut Mathematique, 99 (113) (2016), 243–248.

 

92. E. Kılıç and H. Prodinger,  Closed form evaluation of restricted sums containing squares of Fibonomial coefficients, U.P.B. Sci. Bull., Series A 78(4) (2016), 57—66.

 

93. E. Kılıç and A. Yalçıner, On sums of squares of Fibonomial coefficients by q-calculus,  Asian-European Journal of Mathematics 9 (3) (2016),

 

94. N. Irmak and E. Kılıç, Decompositions of the Cauchy and Ferrers-Jackson polynomials, Mathematical Communications, 21 (2016), 163–170.

 

95. E. Kılıç, Evaluation of sums containing triple aerated generalized Fibonomial coefficients, Mathematica Slovaca 67(2) (2017), 355–370.

 

96. E. Kılıç and H. Prodinger, The matrix of super Patalan numbers and its factorizations, Filomat 31(8) (2017), 2337–2344.

 

97. E. Kılıç and H. Prodinger, Closed form evaluation of Melham's reciprocal sums, Miskolc Mathematical Notes 18 (1) (2017), 251–264.

 

98. E. Kılıç and T. Arıkan, A class of non-symmetric band determinants with the Gaussian q-binomial coefficients, Quaestiones Mathematicae Journal 40(5) 2017, 645–660.

 

99. E. Kılıç and H. Prodinger, Evaluation of sums involving products of Gaussian q-binomial coefficients with applications to Fibonomial sums, Turkish Journal of Mathematics  41 (2017), 707—716.

 

100.  E. Kılıç and I. Akkus, On usual Fibonomial sums identities with special sign functions: anallytically q-calculus approach, accepted in Mathematica Slovaca.

 

101. E. Kılıç and T. Arıkan, Evaluation of hessenberg determinants via generating function approach, accepted in Filomat.

 

102. E. Kılıç, N. Ömür and S. Koparal, On alternating weighted binomial sums with falling factorials, Bulletin of Mathematical Analysis and Applications 9 (1) (2017), 58—64.

 

103. E. Kılıç and T. Arıkan, Double binomial sums and double sums related with certain linear recurrences of various order, accepted in Chiang Mai Journal of Science.

 

104. E. Kılıç, N. Omur and S. Koparal, Formulae for various weighted binomial sums with the falling factorials, accepted in Ars Combinatoria.

 

105. E. Kılıç , T. Mansour and T. Arıkan, A wilf class composed of 19 symmetry classes of quadruples of 4-letter patterns, accepted in Notes on Number Theory and Discrete Mathematics.

 

106. E. Kılıç, Evaluation of various partial sums of Gaussian q-binomial sums, accepted in Arabian Journal of Mathematics.

 

107. E. Kılıç, Three binomial sums weighted by falling and rising factorials, accepted in Turkish Journal of Mathematics.