Applications of Fibonacci Numbers: Volume 5 Proceedings of ‘The Fifth International Conference on Fibonacci Numbers and Their Applications’, The University of St. Andrews, Scotland, July 20–July 24, 1992

Front Matter....Pages i-xxxiv
Multidimensional Golden Means....Pages 1-9
A Necessary and Sufficient Condition that Rays of a Star Configuration on Pascal’s Triangle Cover its Center with Respect to GCD and LCM....Pages 11-36
On the Minimal Center Covering Stars with Respect to GCD in Pascal’s Pyramid and its Generalizations....Pages 37-43
An Extension of an Old Classical Diophantine Problem....Pages 45-48
Fourier Analysis in Finite Nilpotent Groups....Pages 49-59
Wall and Vinson Revisited....Pages 61-68
Designer Decimals: Fractions which Contain Second Order Recursion Sequences in Their Decimal Expansions, Reading Left to Right or Right to Left....Pages 69-75
Semigroup Presentations and Number Sequences....Pages 77-83
Counting the Number of Solutions of Congruences....Pages 85-101
On the Number of Overlapping Success Runs in a Sequence of Independent Bernoulli Trials....Pages 103-112
Embedding Fibonacci Words into Fibonacci Word Patterns....Pages 113-122
On Sums of Cubes of Fibonacci Numbers....Pages 123-136
Integer Sided Triangles Whose Ratio of Altitude to Base is an Integer....Pages 137-142
On a Class of Iterative Recurrence Relations....Pages 143-158
Discrete Operational Calculi for Two-sided Sequences....Pages 159-168
Transformations of Fibonacci-Lucas Identities....Pages 169-184
Fibonacci Numbers and Continued Fraction Expansions....Pages 185-197
The DFF and DFFz Triangles and Their Mathematical Properties....Pages 199-206
Contributions from Cascaded Combinations to the Naming of Special Permutations....Pages 207-215
The Zeckendorf Representation of {F kn /F n }....Pages 217-219
Fractal Patterns Derived from Rational Binomial Coefficients....Pages 221-228
Hausdorff Dimension in Pascal’s Triangle....Pages 229-244
Chaos, Elliptic Curves and All That....Pages 245-256
Co-Related Sequences Satisfying the General Second Order Recurrence Relation....Pages 257-262
On the Moments of the Sum-of-Digits Function....Pages 263-271
Problems on Fibonacci and B-Adic Tree Representations by Regular K-Gons....Pages 273-277
Two-Distance Sets and the Golden Ratio....Pages 279-288
A Fibonacci Problem Classification Scheme Useful to Undergraduate Pedagogy....Pages 289-304
Zeckendorf Representations of Positive and Negative Integers by Pell Numbers....Pages 305-316
Integration Sequences of Fibonacci and Lucas Polynomials....Pages 317-330
Pell-Type Number Generators of Pythagorean Triples....Pages 331-343
Balance Morphology of a Binary Tree....Pages 345-354
Nörlund’s Number B n (n) ....Pages 355-366
On Stirling-Type Pairs and Extended Gegenbauer-Humbert-Fibonacci Polynomials....Pages 367-377
A Sequence Arising from Reflections in Multiple Glass Plates....Pages 379-386
Diophantine Representation of Non-Fibonacci Numbers....Pages 387-392
On Some Problems Related to the Fibonacci Group....Pages 393-397
Congruence Properties of Fibonacci Numbers and Fibonacci Coefficients Modulo p 2 ....Pages 399-403
Orderings of the Set of All Positive Fibonacci Sequences....Pages 405-416
Some Results Concerning the Reciprocal Sum of Prime Divisors of a Lucas Number....Pages 417-420
Rational Numbers with Predictable Engel Product Expansions....Pages 421-427
Two Families of Orthogonal Polynomial Systems Related to Fibonacci Chains....Pages 429-440
On the Formation of Higher Order Higher Dimensional Line-Sequential Vector Spaces....Pages 441-447
Arithmetic Sequences and Second order Recurrences....Pages 449-457
Generalized Fibonacci Pseudoprimes and Probable Primes....Pages 459-464
A Generalization of the Fibonacci Sequence....Pages 465-472
How to Advance on a Stairway by Coin Flippings....Pages 473-479
Fibonacci Sequence and its Generalizations Hidden in Algorithms for Generating Morse Codes....Pages 481-486
On Matrix Representations of Generalized Fibonacci Numbers and Their Applications....Pages 487-496
A Cholesky Decomposition in Matching Insulin Profiles....Pages 497-506
Generalized Exponential and Trigonometric Functions....Pages 507-514
Divisibility of Terms in Lucas Sequences by Their Subscripts....Pages 515-525
Upper Bounds for Frequencies of Elements in Second-Order Recurrences over A Finite Field....Pages 527-546
On the Convergence of Quotients of Some Recursive Sequences....Pages 547-560
Two Distribution Problems for Polynomials....Pages 561-568
The Elements of Enteger Geometry....Pages 569-583
Totient Functions on the Euler Number Tree....Pages 585-600
Using Matrix Techniques to Establish Properties of k-Order Linear Recursive Sequences....Pages 601-615
Back Matter....Pages 617-625