CODING OBJECTS RELATED TO CATALAN NUMBERS 1
... If we have a Catalan sequence, from this the corresponding object can be easily obtained. Let us consider for exemplification the sequence 00010111. If we want to obtain the corresponding binary tree, we shall omit the first 0 and the last 1. The subsequence 00 is for a left edge (in a stack we shal ...
... If we have a Catalan sequence, from this the corresponding object can be easily obtained. Let us consider for exemplification the sequence 00010111. If we want to obtain the corresponding binary tree, we shall omit the first 0 and the last 1. The subsequence 00 is for a left edge (in a stack we shal ...
Ch. 5A Arithmetic Sequences
... This skip counting is a slight variation because the number I am adding to find subsequent terms is not necessarily the first number. All of these examples fit the definition of an Arithmetic Sequence. An arithmetic sequence is a sequence in which every term after the first term is found by adding a ...
... This skip counting is a slight variation because the number I am adding to find subsequent terms is not necessarily the first number. All of these examples fit the definition of an Arithmetic Sequence. An arithmetic sequence is a sequence in which every term after the first term is found by adding a ...
New York Journal of Mathematics Normality preserving operations for
... b-normality preserving. It was shown in [2] that C. Aistleitner’s result does not generalize to at least one notion of normality for some of the Cantor series expansions, which we will be investigating in this paper. There are still many open questions relating to the functions πr and σr . For examp ...
... b-normality preserving. It was shown in [2] that C. Aistleitner’s result does not generalize to at least one notion of normality for some of the Cantor series expansions, which we will be investigating in this paper. There are still many open questions relating to the functions πr and σr . For examp ...
Recursive definitions A sequence is defined recursively if (B) some
... previous numbers in the sequence. Such relations often describe (dynamical) systems that evolve over time, as well as determining the number of steps in algorithmic computations. An example of a recurrence relation is an = 3an-1 , for n $ 1. If the starting point a0 is given as 2, then the sequence ...
... previous numbers in the sequence. Such relations often describe (dynamical) systems that evolve over time, as well as determining the number of steps in algorithmic computations. An example of a recurrence relation is an = 3an-1 , for n $ 1. If the starting point a0 is given as 2, then the sequence ...
Sequence
In mathematics, a sequence is an ordered collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers.For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). In computing and computer science, finite sequences are sometimes called strings, words or lists, the different names commonly corresponding to different ways to represent them into computer memory; infinite sequences are also called streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.