FindSequenceFunction

FindSequenceFunction[{a1, a2, a3, ...}]
attempts to find a simple function that yields the sequence when given successive integer arguments.

FindSequenceFunction[{{n1, a1}, {n2, a2}, ...}]
attempts to find a simple function that yields when given argument .

FindSequenceFunction[list, n]
gives the function applied to n.

Details and OptionsDetails and Options

  • 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:
  • FunctionSpaceAutomaticwhere to look for candidate simple functions
    MethodAutomaticmethod to use
    TimeConstraint10how many seconds to search a particular function space or perform a transformation
    ValidationLengthAutomaticsequence 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.

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

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

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

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Check the even subsequence:

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