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FindSequenceFunction

FindSequenceFunction

attempts to find a simple function that yields the sequence

when given successive integer arguments.

FindSequenceFunction

attempts to find a simple function that yields

when given argument

.

FindSequenceFunction

gives the function applied to n.

MORE INFORMATION

The sequence elements can be either exact numbers or symbolic expressions.

FindSequenceFunction finds results in terms of a wide range of integer functions, as well as implicit solutions to difference equations represented by DifferenceRoot.

If FindSequenceFunction cannot find a simple function that yields the specified sequence, it returns unevaluated.

The following options can be used:

	FunctionSpace	Automatic	where to look for candidate simple functions
	Method	Automatic	method to use
	TimeConstraint	10	how many seconds to search a particular function space or perform a transformation
	ValidationLength	Automatic	sequence length used to validate a candidate function found

FindSequenceFunction[list] by default uses earlier elements in list to find candidate simple functions, then validates the functions by looking at later elements.

FindSequenceFunction[list] only returns functions that correctly reproduce all elements of list.

Basic Examples (2)

Find a sequence that yields the sequence 1,1,2,3,5,8,13,...:

Find a function that yields the given sequence as a subsequence:

Check the even subsequence:

Find a sequence that yields the sequence 1,1,2,3,5,8,13,...:

Out[1]=

Out[2]=

Find a function that yields the given sequence as a subsequence:

Out[1]=

Out[2]=

Check the even subsequence:

Out[3]=

Periodic sequences:

Polynomial functions:

Rational functions:

Hypergeometric terms:

Recurrence equations:

Generalizations & Extensions (1)

FindSequenceFunction works on arbitrary exact numbers or symbolic expressions:

Applications (5)

Find formulas for complex sequences:

Use additional values to validate the result:

Find a closed form for a sequence of definite integrals:

Find a closed form for the number of 0,1 sequences of length

containing two adjacent 1s:

Generate a sequence from a power series expansion:

Find its formula:

Use SeriesCoefficient to find an alternative formula:

FindSequenceFunction assumes that sequences start with index 1:

Compare the result:

Compute a finite number of Fourier coefficients:

Find the formula:

Use a FourierCoefficient directly:

Verify the consistency of formulas:

Properties & Relations (2)

Sum, Product, and other general discrete functions may be used:

Find the generating function of a sequence:

Use FindGeneratingFunction:

FindLinearRecurrence FindGeneratingFunction Interpolation InterpolatingPolynomial RSolve Rationalize RootApproximant DifferenceRoot

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