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An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.
Fibonacci sequence. In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted Fn . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 [1][2] and some (as ...
Objects studied in discrete mathematics include integers, graphs, and statements in logic. [1][2][3] By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized ...
v − 1. Chromatic number. 2 if v > 1. Table of graphs and parameters. In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently ...
An integer sequence is a sequence whose terms are integers. A polynomial sequence is a sequence whose terms are polynomials. A positive integer sequence is sometimes called multiplicative, if a nm = a n a m for all pairs n, m such that n and m are coprime. [8] In other instances, sequences are often called multiplicative, if a n = na 1 for all n.
The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs. He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009. [4] Sloane is the chairman of the OEIS Foundation.
Lucas number. Infinite integer series where the next number is the sum of the two preceding it. The Lucas spiral, made with quarter- arcs, is a good approximation of the golden spiral when its terms are large. However, when its terms become very small, the arc's radius decreases rapidly from 3 to 1 then increases from 1 to 2.
Arithmetic progression. An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.