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1 INDEX OF AUTHORS A Abderrezzak, Abdelhamid Multivariate Symmetric Identities 34.5(1996)386 Abercrombie, Alexander G. Letter: Prime Factors of Fx(p), where p is prime 3.2(1975)171 Abrahams, Julia Coupled Sequences of Generalized Fibonacci Trees and Unequal Costs Coding Problems 35.4(1997)309 Nonexhaustive Generalized Fibonacci Trees in Unequal Costs Coding Problem 38.2(2000)127 Varn Codes and Generalized Fibonacci Trees 33.1(1995)21 Abramson, Morton Combinations, Compositions and Occupancy Problems 9.3(1971)225 Restricted Combinations and Compositions 14.5(1976)439 Abrate, Marco Fibonacci Sequences of Quaternions 46/47.4(2008/2009)356 Acosta-de-Orozco, Maria T. & Gomez-Calderon, J. Local Minimal Polynomials over Finite Fields 34.2(1996)139 Andaloro, Paul On Total Stopping Times Under 3x + 1 Iteration 38.1(2000)73 Adelberg, Arnold Higher Order Bernoulli Polynomials and Newton Polygons, PVII(1998)1 Universal Bernoulli Polynomials and P-Adic Congruences, PIX(2004)1 Adiga, Chandrashekar & Bhargava, S. & Somashekara, D.D. Three-Square Theorem as an Application of Andrew's Identity 31.2(1993)129 Somashekara, D.D. & Bhargava, S. Three-Square Theorem as an Application of Andrew's Identity 31.2(1993)129 Adikesavan, A.S. & Narayanaswami, S. Modification of Goka's Binary Sequence, A 17.3(1979)212 Adler, Irving Concerning the Divisors of N and the Exponents they Belong to Modulo (N-1) or (N + 1)27.3(1989)259 Sequences with a Characteristic Number 9.2(1971)147; Shorter Proof, A 7.5(1969)538 Simple Continued Fraction Represents a Mediant Nest of Intervals, A 16.6(1978)527 Three Diophantine Equations, Part I: 6.6(1968)360; Part II: 7.2(1969)181 Agarwal, A.K. Combinatorial Interpretations of the q-Analogues of L2n+1 29.2(1991)137 Note on n(x,y)-Reflected Lattice Paths A, 25.4(1987)317 On a New Kind of Numbers 28.3(1990)194 Properties of a Recurring Sequence 27.2(1989)169 INDEX OF AUTHORS 2 A Agratini, Octavian Generalization of Durrmeyer-Type Polynomials and Their Approximation Properties, A, PIX(2004)9 Aho, A.V. & Sloane, N.J.A. Some Doubly Exponential Sequences 11.4(1973)429 Ahuja, J.C. Orthogonal Expansion Derived from the Extreme Value Distribution 7.5(1969)488 Ahuja, J.C. & Enneking, E.A. Concavity Property and a Recurrence Relation for Associated Lah Numbers 17.2(1979)158 Generalized Bell Numbers 14.1(1976)67 Nash, S.W. Note on Orthogonal Polynomials, A 4.1(1966)49 Aiello, W. & Hardy, G.E. & Subbarao, M.V. On the Existence of e-Multiperfect Numbers 25.1(1987)65 Subbarao, M.V. & Hardy, G.E. On the Existence of e-Multiperfect Numbers 25.1(1987)65 Ainsworth, O.R. On Generating Functions 15.2(1977)161 Ainsworth, O.R. & Morris, J.E., Jr. Property of Quasi-Orthogonal Polynomials, A 18.2(1980)163 Neggers, J. Family of Polynomials and Powers of the Secant, A 21.2(1983)132 Akritas, Alkiviadis G. Sylvester's Forgotten Form of the Resultant 31.4(1993)325 Akritas, A.G. & Bradford, P.G. Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations, The, PIII(1990)1 Alameddine, A.F. Fibonacci Numbers and Bipyramids 27.3(1989)247 Alberti, Furio Another Proof for a Continued Fraction Identity 11.5(1973)533 Root Property of a Psi-Type Equation, A 19.1(1981)56 Alder, Henry L. &[ Lewis, J.K. & Muwafi, A.A. Euler's Partition Identity-Are there Any More Like it? 23.2(1985)113 3 INDEX OF AUTHORS A Alder, Henry L. & Muwafi, Amin A. Generalizations of Euler's Recurrence Formula for Partitions 13.4(1975)337 Identities Relating to the Number of Partitions into an Even and Odd Number of Parts 13.2(1975)147 Muwafi, A.A. & Lewis, J.K. Euler's Partition Identity-Are there Any More Like it? 23.2(1985)113 Alexanderson, G.L. & Hillman, A.P. Motivation for Continued Fractions, A 2.2(1964)145 Hoggatt, V.E., Jr. Property of Multinomial Coefficients, A 9.4(1971)351 Sums of Partition Sets in Generalized Pascal Triangles I, 14.2(1976)117 Klosinski, L.F. Fibonacci Analogue of Gaussian Binomial Coefficients, A 12.2(1974)129 Alford, Cecil O. & Fielder, D.C. Contributions from Cascaded Combinations to the Naming of Special Permutations, PV(1993)207 Investigating Special Binary Sequences with Some Computer Help, PVIII(1999)121 Investigation of Sequences Derived from Hoggatt Sums and Hoggatt Triangles, An, PIII(1990)77 More Applications of a Partition Driven Symmetric Table, PVI(1996)93 Observations from Computer Experiments on an Integer Equation, PVII(1998)93 On a Conjecture by Hoggatt with Extensions to Hoggatt Sums and Hoggatt Triangles 27.2(1989)160 Pascal's Triangle: Top Gun or Just One of the Gang, PIV(1991)77 Alfred, U., Br. (Also see under Brousseau, Alfred, Br) Additional Factors of the Fibonacci and Lucas Series 1.1(1963)34 Book Reviews: Recurring Sequences by Dov Jarden 4.3(1966)208; 5.4(1967)328 Algebra Through Problem Solving by Abraham P. Hillman 4.3(1966)264 Continued Fractions of Fibonacci and Lucas Ratios 2.4(1964)269 Digit Muses, A 2.3(1964)210; Errata 3.1(1965)66 Dying Rabbit Problem Revived 1.4(1963)53 Exploring Fibonacci Magic Squares 2.3(1964)216 Fibonacci Numbers 1.1(1963)57 Fibonacci Numbers with a Calculator 2.2(1964)138 Fibonacci Polygons 1.3(1963)60 Fibonacci Representation of Integers, The 1.4(1963)72; 2.2(1964)114 INDEX OF AUTHORS 4 A Alfred, U., Br. (Cf. Brousseau, Alfred, Br) Exploring Fibonacci Residues 2.1(1964)42 Generalized Fibonacci-Lucas Relations 3.4(1965)319 Geometric-Algebraic Fibonacci Patterns 2.4(1964)318 Recurrent Sequences 1.2(1963)81; Errata 2.1(1964)66 Special Fibonacci Relations 4.3(1966)262 Math Morals 3.1(1965)53 Note on Third Order Determinants 3.1(1965)59 On Square Lucas Numbers 2.1(1964)11 On the Form of Primitive Factors of Fibonacci Numbers 1.1(1963)43 On the Ordering of Fibonacci Sequences 1.4(1963)43; Errata 2.1(1964)38 Periodic Properties of Fibonacci Summations 1.3(1963)33 Primes which Are Factors of All Fibonacci Sequences 2.1(1964)33 Seeking the Lost Gold Mine or Exploring for Fibonacci Factorizations 3.2(1965)129 Some Determinants Involving Powers of Fibonacci Numbers 2.2(1964)81 Strip Method of Summing Linear Fibonacci Expressions, A 3.3(1965)224 Alladi, Krishnaswami Approximation of Irrationals with Farey Fibonacci Fractions 13.3(1975)255 Farey Sequence of Fibonacci Numbers, A 13.1(1975)1 On Polynomials Generated by Triangular Arrays 14.5(1976)461 On the Probability that n and Ù(n)Are Relatively Prime 19.3(1981)228 Rapid Method to Form Farey Fibonacci Fractions, A 13.1(1975)31 Alladi, Krishnaswami & Hoggatt, V.E., Jr. Compositions and Recurrence Relations Part I: Compositions with Ones and Twos 13.3(1975)233; Part II: 15.3(1977)239 Compositions with Ones and Twos 13.3(1975)233 Generalized Fibonacci Tiling 13.2(1975)137 In-Winding Spirals 14.2(1976)144 Limiting Ratios of Convolved Recursive Sequences 15.3(1977)211 On Tribonacci Numbers and Related Functions 15.1(1977)42 Shannon, A.G. On a Property of Consecutive Farey-Fibonacci Fractions 15.2(1977)153 Alameddine, Ahmad Fawzi Bounds on the Fibonacci Number of a Maximal Outerplanar Graph 36.3(1998)206 Allard, A. & Lecomte, P. Periods and Entry Points in Fibonacci Sequence 17.1(1979)51 5 INDEX OF AUTHORS A Allen, H.D. Metric Paper to Fall Short of "Golden Mean" 15.3(1977)220 Almkvist, Gert Solution to a Tantalizing Problem, A 24.4(1986)316 Alonso, James Arithmetic Sequences of Higher Order 14.2(1976)147 Al-Salam, Nadhla A. Some Operational Formulas for the q-Laguerre Polynomials 22.2(1984)166 Al-Salam, W.A. & Verma, A. Fibonacci Numbers and Eulerian Polynomials 9.1(1971)18 Alspach, Brian & Heinrich, K. Perfect Magic Cubes of Order 4m 19.2(1981)97 Altevogt, Rudolf & Davis, T.A. Golden Mean of the Human Body 17.4(1979)340 Altimi ik, E. & Dursun, T. On the Almost Hilbert-Smith Matrices 40.4(2002)339 Alvfeldt, Olov Brain Teaser Related to Fibonacci Numbers, A 7.3(1969)310 Anatassova, Vassia K. & Turner, J.C. On Triangles and Squares Marked with Goldpoints - Studies of Golden Tiles, PVIII(1999)11 Anaya, Janet Crump & Hoggatt, V.E., Jr. Primer for the Fibonacci Numbers, A, Part XI: Multisection Generating Functions for the Columns of Pascal's Triangle 11.1(1973)85 Anaya, Robert & Crump, J. Generalized Greatest Integer Function Theorem, A 10.2(1972)207 Andaloro, Paul J. 3x + 1 Problem and Directed Graphs The 40.1(2002)43 Andersen, Harold & Brousseau, Alfred, Br. & Povse, J. Curious Property of Unit Fractions of the Form 1/d where (d,10) = 1, A 11.1(1973)91 Povse, J. & Brousseau, Alfred, Br. Curious Property of Unit Fractions of the Form 1/d where (d,10) = 1, A 11.1(1973)91 INDEX OF AUTHORS 6 A Anderson, David A. & Loyer, M.W. Diophantine Equation Nb22 = c + N + 1, The 17.1(1979)69 Anderson, Jean H. Spirals, Checkerboards, Polyominoes, and the Fibonacci Sequence 8.1(1970)90 Anderson, O.D. Some More Patterns from Pascal's Triangle 16.4(1978)296 Anderson, Peter G. Advances in Linear Pixel Shuffling, PVI(1996)1 Anderson, Peter G. Book Review: Proofs that Really Count: The Art of Combinatorial Proof by Arthur T.
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  • On H(X)-Fibonacci Octonion Polynomials, Ahmet Ipek & Kamil

    On H(X)-Fibonacci Octonion Polynomials, Ahmet Ipek & Kamil

    Alabama Journal of Mathematics ISSN 2373-0404 39 (2015) On h(x)-Fibonacci octonion polynomials Ahmet Ipek˙ Kamil Arı Karamanoglu˘ Mehmetbey University, Karamanoglu˘ Mehmetbey University, Science Faculty of Kamil Özdag,˘ Science Faculty of Kamil Özdag,˘ Department of Mathematics, Karaman, Turkey Department of Mathematics, Karaman, Turkey In this paper, we introduce h(x)-Fibonacci octonion polynomials that generalize both Cata- lan’s Fibonacci octonion polynomials and Byrd’s Fibonacci octonion polynomials and also k- Fibonacci octonion numbers that generalize Fibonacci octonion numbers. Also we derive the Binet formula and and generating function of h(x)-Fibonacci octonion polynomial sequence. Introduction and Lucas numbers (Tasci and Kilic (2004)). Kiliç et al. (2006) gave the Binet formula for the generalized Pell se- To investigate the normed division algebras is greatly a quence. important topic today. It is well known that the octonions The investigation of special number sequences over H and O are the nonassociative, noncommutative, normed division O which are not analogs of ones over R and C has attracted algebra over the real numbers R. Due to the nonassociative some recent attention (see, e.g.,Akyigit,˘ Kösal, and Tosun and noncommutativity, one cannot directly extend various re- (2013), Halici (2012), Halici (2013), Iyer (1969), A. F. Ho- sults on real, complex and quaternion numbers to octonions. radam (1963) and Keçilioglu˘ and Akkus (2015)). While ma- The book by Conway and Smith (n.d.) gives a great deal of jority of papers in the area are devoted to some Fibonacci- useful background on octonions, much of it based on the pa- type special number sequences over R and C, only few of per of Coxeter et al.