Constant-recursive sequence and Generating function

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Difference between Constant-recursive sequence and Generating function

Constant-recursive sequence vs. Generating function

In mathematics, an infinite sequence of numbers s_0, s_1, s_2, s_3, \ldots is called constant-recursive if it satisfies an equation of the form for all n \ge d, where c_i are constants. In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.

Binomial transform

In combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences.

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Catalan number

In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects.

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Cauchy product

In mathematics, more specifically in mathematical analysis, the Cauchy product is the discrete convolution of two infinite series.

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Closed-form expression

In mathematics, an expression is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations (and integer powers) and function composition.

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Coefficient

In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or an expression.

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Combinatorics

Combinatorics is an area of mathematics primarily concerned with the counting, selecting and arranging of objects, both as a means and as an end in itself.

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Degree of a polynomial

In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients.

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Fibonacci sequence

In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones.

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Finite difference

A finite difference is a mathematical expression of the form.

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Generating function transformation

In mathematics, a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating function enumerating another.

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Geometric progression

A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Number theory

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.

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Rational function

In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials.

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Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

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Square number

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself.

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Triangular number

A triangular number or triangle number counts objects arranged in an equilateral triangle.

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