Geodesic

Sommaire du Fascicule no. 1

On the lcm-sum function
Enumeration of edges in some lattices of paths
On the log-concavity of the hyperfibonacci numbers and the hyperlucas numbers
A new approach to multivariate $q$-Euler polynomials using the umbral calculus
On the number of fixed-length semiorders
On a conjecture of Farhi
Periodicity of the last digits of some combinatorial sequences
On a congruence of Kimball and Webb involving Lucas sequences

Sommaire du Fascicule no. 2

Constructing exponential Riordan arrays from their $A$ and $Z$ sequences
Bernoulli numbers and a new binomial transform identity
Generalized Stirling numbers, exponential Riordan arrays, and Toda chain equations
Some identities for Fibonacci and incomplete Fibonacci $p$-numbers via the symmetric matrix method
On the number of polynomials of bounded height that satisfy the Dumas criterion
Asymptotic expansions of central binomial coefficients and Catalan numbers
Extremely abundant numbers and the Riemann hypothesis
Tilings, continued fractions, derangements, scramblings, and $e$

Sommaire du Fascicule no. 3

Fermat numbers in multinomial coefficients
GCD property of the generalized star of David in the generalized Hosoya triangle
Addition chains meet postage stamps: reducing the number of multiplications
The number of relatively prime subsets of a finite union of sets of consecutive integers
A counting function generalizing binomial coefficients and some other classes of integers
Complementary Bell numbers and $p$-adic series
The 1-box pattern on pattern-avoiding permutations
Dickson polynomials, Chebyshev polynomials, and some conjectures of Jeffery

Sommaire du Fascicule no. 4

Incomplete tribonacci numbers and polynomials
On error sums for square roots of positive integers with applications to Lucas and Pell numbers
Combinatorial expressions involving Fibonacci, hyperfibonacci, and incomplete Fibonacci numbers
A short proof of Carlitz's Bernoulli number identity
Some formulas for a family of numbers analogous to the higher-order Bernoulli numbers
Cyclic products of purely periodic irrationals
A simplified binet formula for $k$-generalized Fibonacci numbers
Multi-poly-Bernoulli numbers and finite multiple zeta values

Sommaire du Fascicule no. 5

More determinant representations for sequences
Iterative procedure for hypersums of powers of integers
Combinatorial proofs of some formulas for triangular tilings
Comparing two matrices of generalized moments defined by continued fraction expansions
A combinatorial proof of the log-convexity of Catalan-like numbers
On reciprocity formulas for Apostol's Dedekind sums and their analogues
Wythoff Nim extensions and splitting sequences
A note on the conjecture of Ramirez and Sirvent

Sommaire du Fascicule no. 6

On the average path length of complete $m$-ary trees
A simpler normal number construction for simple Lüroth series
On integral points on biquadratic curves and near-multiples of squares in Lucas sequences
On an arithmetic convolution
A meet-in-the-middle algorithm for finding extremal restricted additive 2-bases
Finite reciprocal sums involving summands that are balanced products of generalized Fibonacci numbers
Counting palindromes according to $r$-runs of ones using generating functions
Generating functions for extended Stirling numbers of the first kind

Sommaire du Fascicule no. 7

$p$-adic properties of Lengyel's numbers
Nim fractals
Largest values for the stern sequence
On the asymptotic behavior of Dedekind sums
Asymptotic series for Hofstadter's figure-figure sequences
Representing integers as the sum of two squares in the ring $\Bbb Z_n$
An elementary proof that any natural number can be written as the sum of three terms of the sequence $\lfloor \frac{n}{2/3} \rfloor $
On a new collection of words in the Catalan family

Sommaire du Fascicule no. 8

Congruences involving sums of ratios of Lucas sequences
On the powerful and squarefree parts of an integer
Free Fibonacci sequences
Prisoners and guards on rectangular boards
On the Dirichlet convolution of completely additive functions
On a congruence modulo $n^3$ involving two consecutive sums of powers
A new kind of Fibonacci-like sequence of composite numbers
Powers of two as sums of two Lucas numbers

Sommaire du Fascicule no. 9

On the ratio of the sum of divisors and Euler's totient function. II.
A famous identity of Hajós in terms of sets
Higher order derivatives of trigonometric functions, Stirling numbers of the second kind, and Zeon algebra

Sommaire du Fascicule no. 10

The 2-adic order of the tribonacci numbers and the equation $T_n = m!$