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Volume 52 Number 5
(Special Open Access Issue)
December 2014

Proceedings

of the 16th International Conference
on Fibonacci Numbers and Their Applications

Rochester Institute of Technology, Rochester, New York
July 20–27, 2014

Edited by Peter G. Anderson, Christian Ballot, and William Webb


CONTENTS

Cover page i

Introduction iii

Foreword v

Table of Contents vii

Marjorie Bicknell-Johnson
The Fibonacci Association: Historical Snapshots
1
     Full text

Clark Kimberling, Problem Editor
ProblemProposals
5
     Full text

Peter G. Anderson
More Properties of the Zeckendorf Array
15
     Full text

Krassimir T. Atanassov, Daryl R. DeFord, and Anthony G. Shannon
Pulsated Fibonacci Recurrences
22
     Full text

Arthur T. Benjamin and Elizabeth Reiland
Combinatorial Proofs of Fibonomial Identities
28
     Full text

Andrew Best, Patrick Dynes, Xixi Edelsbrunner, Brian McDonald, Steven J. Miller, Kimsy Tor, Caroline Turnage-Butterbaugh, and Madeleine Weinstein
Benford Behavior of Zeckendorf Decompositions
35
     Full text

Andrew Best, Patrick Dynes, Xixi Edelsbrunner, Brian McDonald, Steven J. Miller, Kimsy Tor, Caroline Turnage-Butterbaugh, and Madeleine Weinstein
Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals
47
     Full text

Daniel Birmajer, Juan B. Gil, and Michael D. Weiner
Convolutions of Tribonacci, Fuss-Catalan, and Motzkin Sequences
54
     Full text

Jens-P. Bode and Heiko Harborth
Steinhaus Triangles with Generalized Pascal Addition
61
     Full text

Minerva Catral, Pari Ford, Pamela Harris, Steven J. Miller, and Dawn Nelson
Generalizing Zeckendorf’s Theorem: The Kentucky Sequence
68
     Full text

Curtis Cooper
Algebraic Statements Similar to Those in Ramanujan’s "Lost Notebook"
91
     Full text

Daryl DeFord
Enumerating Distinct Chessboard Tilings
102
     Full text

M. Cetin Firengiz and Naim Tuglu
On the q-Seidel Matrix
117
     Full text

Russell Jay Hendel
A Cayley-Hamilton and Circulant Approach to Jump Sums
124
     Full text

Clark Kimberling and Peter J. C. Moses
The Infinite Fibonacci Tree and Other Trees Generated by Rules
136
     Full text

Takao Komatsu, Zuzana Masáková, and Edita Pelantová
Higher-Order Identities for Fibonacci Numbers
150
     Full text

Florian Luca and Pantelimon Stănică
On Fibonacci Numbers which are Elliptic Korselt Numbers
164
     Full text

Sam Northshield
Three Analogues of Stern’s Diatomic Sequence
168
     Full text

G. K. Panda and A. K. Panda
Balancing-like Sequences Associated with Integral Standard Deviations of Consecutive Natural Numbers
187
     Full text

Pantelimon Stănică
Normic Continued Fractions in Totally and Tamely Ramified Extensions of Local Fields
193
     Full text

William Webb and Nathan Hamlin
Compositions and Recurrences
201
     Full text

Paul Thomas Young
Symmetries of Stirling Number Series
205
     Full text

Yifan Zhang and George Grossman
Diophantine Triples and the Extendibility of {1, 2, 5}, {1, 5, 10}
212
     Full text

Conference Participants 216