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Unlike the preceding sequence, this sequence does not have any pattern that is easily discernible by inspection. Other examples are sequences of functions, whose elements are functions instead of numbers. The On-Line Encyclopedia of Integer Sequences comprises a large list of examples of integer sequences. [3]
Recamán's sequence: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence. A005132: Look-and ...
Visible patterns in nature are governed by physical laws; for example, meanders can be explained using fluid dynamics. In biology , natural selection can cause the development of patterns in living things for several reasons, including camouflage , [ 26 ] sexual selection , [ 26 ] and different kinds of signalling, including mimicry [ 27 ] and ...
In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers , commonly denoted F n .
For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with a common ratio of 1/2. Examples of a geometric sequence are powers r k of a fixed non-zero number r, such as 2 k and 3 k. The general form of a geometric sequence is
A pattern is a regularity in the world, in human-made design, [1] or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design. Any of the senses may directly observe patterns.
Other examples are regression, which assigns a real-valued output to each input; [1] sequence labeling, which assigns a class to each member of a sequence of values [2] (for example, part of speech tagging, which assigns a part of speech to each word in an input sentence); and parsing, which assigns a parse tree to an input sentence, describing ...
Fixed action pattern" is an ethological term describing an instinctive behavioral sequence that is highly stereotyped and species-characteristic. [1] Fixed action patterns are said to be produced by the innate releasing mechanism, a "hard-wired" neural network , in response to a sign/key stimulus or releaser .