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Discrete Calculus
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FindLinearRecurrence
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BUILT-IN MATHEMATICA SYMBOL
LinearRecurrence
FindSequenceFunction
NullSpace
See Also »
|
Discrete & Integer Data
Discrete Calculus
Integer Sequences
Recurrence and Sum Functions
Summary of New Features in 7.0
New in 7.0: Alphabetical Listing
New in 7.0: Mathematics & Algorithms
More About »
FindLinearRecurrence
FindLinearRecurrence
[
list
]
finds if possible the minimal linear recurrence that generates
list
.
FindLinearRecurrence
finds if possible the linear recurrence of maximum order
d
that generates
list
.
MORE INFORMATION
FindLinearRecurrence
gives the shortest kernel
ker
which reproduces
list
from
LinearRecurrence
. The initial list
init
comes from the first elements in
list
.
FindLinearRecurrence
[
list
]
will find the coefficients
such that
LinearRecurrence
[{
a
1
,
...
,
a
d
},
list
[[1;;
d
]],
Length
[
list
]]
generates
list
.
EXAMPLES
CLOSE ALL
Basic Examples
(3)
Find linear recurrences for simple sequences:
Generate data from a linear recurrence:
Find the underlying recurrence equation:
Use symbolic data:
Find linear recurrences for simple sequences:
In[1]:=
Out[1]=
In[2]:=
Out[2]=
In[3]:=
Out[3]=
Generate data from a linear recurrence:
In[1]:=
Out[1]=
Find the underlying recurrence equation:
In[2]:=
Out[2]=
Use symbolic data:
In[1]:=
Out[1]=
In[2]:=
Out[2]=
SEE ALSO
LinearRecurrence
FindSequenceFunction
NullSpace
MORE ABOUT
Discrete & Integer Data
Discrete Calculus
Integer Sequences
Recurrence and Sum Functions
Summary of New Features in 7.0
New in 7.0: Alphabetical Listing
New in 7.0: Mathematics & Algorithms
New in 7