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"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.
Michael Stifel published the following method in 1544. [3] [4] Consider the sequence of mixed numbers,,,, … with = + +.To calculate a Pythagorean triple, take any term of this sequence and convert it to an improper fraction (for mixed number , the corresponding improper fraction is ).
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.
For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is and the common difference of successive members is , then the -th term of the sequence is given by
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
The algorithm is as follows: [2] Choose any natural number in a given number base.This is the first number of the sequence. Create a new number by sorting the digits of in descending order, and another number by sorting the digits of in ascending order.
Angel numbers are repeating number sequences, often used as guides for deeper spiritual exploration. Ranging from 000 to 999 , each sequence carries its own distinct meaning and energy.
) of a sequence with ordinary generating function G(a n; x) has the generating function (;) because 1 / 1 − x is the ordinary generating function for the sequence (1, 1, ...). See also the section on convolutions in the applications section of this article below for further examples of problem solving with convolutions of generating ...
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