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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
30 is a square pyramidal number. 30 is an even, composite, pronic number.With 2, 3, and 5 as its prime factors, it is a regular number and the first sphenic number, the smallest of the form , where r is a prime greater than 3.
1, 3, 21, and 55 are the only triangular Fibonacci numbers, which was conjectured by Vern Hoggatt and proved by Luo Ming. [53] No Fibonacci number can be a perfect number. [54] More generally, no Fibonacci number other than 1 can be multiply perfect, [55] and no ratio of two Fibonacci numbers can be perfect. [56]
Less common is a two-way distinction between general and singulative. No language has this as its default number contrast, although some languages have specific nouns with this distinction. [198] For example, in Sidama: [199] goto - "hyena(s)" (general) gotiiččo - "hyena" (singulative)
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.
This problem in its most general form is as follows: There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost and profit that may vary depending on the agent-task assignment. Moreover, each agent has a budget and the sum of the costs of tasks assigned to it cannot exceed this budget.
This is a (dualized) (1 + 1)-dimensional case, for a 1-form (dualized because it is a statement about vector fields). This special case is often just referred to as Stokes' theorem in many introductory university vector calculus courses and is used in physics and engineering.