({{, (RefLink[FindLinearRecurrence, paclet:ref/FindLinearRecurrence])[list] 
finds if possible the minimal linear recurrence that generates list.}, {, (RefLink[FindLinearRecurrence, paclet:ref/FindLinearRecurrence])[list,d]
finds if possible the linear recurrence of maximum order d that generates list.}})

OpenersNotesSection(Spacer1)Details

(RefLink[FindLinearRecurrence, paclet:ref/FindLinearRecurrence]) gives the shortest kernel ker which reproduces list from (RefLink[LinearRecurrence, paclet:ref/LinearRecurrence])[ker,init,…]. The initial list init comes from the first elements in list.

(RefLink[FindLinearRecurrence, paclet:ref/FindLinearRecurrence])[list] will find the coefficients {(Subscript[a, 1]),…,(Subscript[a, d])} such that (RefLink[LinearRecurrence, paclet:ref/LinearRecurrence])[{(Subscript[a, 1]),…,(Subscript[a, d])},list[[1;;d]],(RefLink[Length, paclet:ref/Length])[list]] generates list.

OpenersPrimaryExamplesSection(Spacer1)Examples  (3)

OpenersExampleSection0(Spacer1)Basic Examples  (3)

Find linear recurrences for simple sequences:

FindLinearRecurrence[Table[2^k,{k,10}]]

FindLinearRecurrence[Table[Fibonacci[k],{k,10}]]

FindLinearRecurrence[Table[Fibonacci[k] Fibonacci[k-1]^2,{k,10}]]

Generate data from a linear recurrence:

data=LinearRecurrence[{4,3,2,1},{1,2,3,4},10]

Find the underlying recurrence equation:

FindLinearRecurrence[data]

Use symbolic data:

data=Simplify@LinearRecurrence[{4,3,2,1},{a,b,c,d},10]

FindLinearRecurrence[data]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[LinearRecurrence, paclet:ref/LinearRecurrence])  ▪  (RefLink[FindSequenceFunction, paclet:ref/FindSequenceFunction])  ▪  (RefLink[FindTransientRepeat, paclet:ref/FindTransientRepeat])  ▪  (RefLink[NullSpace, paclet:ref/NullSpace])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Integer Sequences, paclet:guide/IntegerSequences])}, {▪(RefLinkPlain[Recurrence and Sum Functions, paclet:guide/RecurrenceAndSumFunctions])}, {▪(RefLinkPlain[Discrete Calculus, paclet:guide/DiscreteCalculus])}, {▪(RefLinkPlain[Discrete & Integer Data, paclet:guide/DiscreteAndIntegerData])}})}})