Related papers: Integers represented by Lucas sequences
We improve lower bounds on the $k$th-order nonlinear complexity of pseudorandom sequences over finite fields and we establish a probabilistic result on the behavior of the $k$th-order nonlinear complexity of random sequences over finite…
We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
We consider cubic number fields ordered by their discriminants, and show that there exist arbitrarily long sequences that contain only fields with class numbers greater than a given bound.
In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes $p$ satisfies congruences that are analogous to Lucas' theorem for the binomial coefficients…
Classical computations can not capture the essence of infinite computations very well. This paper will focus on a class of infinite computations called convergent infinite computations}. A logic for convergent infinite computations is…
Affine $\lambda$-terms are $\lambda$-terms in which each bound variable occurs at most once and linear $\lambda$-terms are $\lambda$-terms in which each bound variables occurs once. and only once. In this paper we count the number of closed…
Let s and t be variables. Define polynomials {n} in s, t by {0}=0, {1}=1, and {n}=s{n-1}+t{n-2} for n >= 2. If s, t are integers then the corresponding sequence of integers is called a Lucas sequence. Define an analogue of the binomial…
The sequence starts with a(1) = 1; to extend it one writes the sequence so far as XY^k, where X and Y are strings of integers, Y is nonempty and k is as large as possible: then the next term is k. The sequence begins 1, 1, 2, 1, 1, 2, 2, 2,…
We show that, if an integer sequence is given by a linear recurrence of constant rational coefficients, then it can be represented as the difference of two arithmetic terms with exponentiation, which do not contain any irrational constant.…
We introduce a transformation of finite integer sequences, show that every sequence eventually stabilizes under this transformation and that the number of fixed points is counted by the Catalan numbers. The sequences that are fixed are…
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…
We count the number of subsets of $\{1,2,\cdots,n\}$ under different conditions and study the sequence obtained as we let $n$ increase.
This paper first discusses the size and orientation of hat supertiles. Fibonacci and Lucas sequences, as well as a third integer sequence linearly related to the Lucas sequence are involved. The result is then generalized to any aperiodic…
We investigate the existence of representations of every large positive integer as a sum of $k$-th powers of integers represented as certain diagonal forms. In particular, we consider a family of diagonal forms and discuss the problem of…
Let $\{U_n\}_{n \geq 0}$ and $\{V_m\}_{m \geq 0}$ be two linear recurrence sequences. We establish an asymptotic formula for the number of integers $c$ in the range $[-x, x]$ which can be represented as differences $ U_n - V_m$. In…
In this paper, we first give a new result characterizing the strongly connected digraphs with a diameter equal to that of their line digraphs. Then, we introduce the concepts of the inner diameter and inner radius of a digraph and study…
This paper generalizes and unifies the existing spectral bounds on the $k$-independence number of a graph, which is the maximum size of a set of vertices at pairwise distance greater than $k$. The previous bounds known in the literature…
We study part sizes of supercritical locally restricted sequential structures. This extends previous results about locally restricted integer compositions and part sizes in smooth supercritical compositional structures. Applications are…
We present a technique for rendering limit sets for kleinian groups, based upon the base transformation of integers and which aims at saving memory resources and being faster than the traditional dictionary based approach.