6.13.4 Table of values and graph of a recurrent sequence: tableseq
The tableseq command fills a column of a spreadsheet with a
recurrence relation. The spreadsheet can be opened with
Alt+t (see Section 4.5).
tableseq takes three arguments, which can be different
depending on how many terms are involved in the recurrence relation.
For a one term recurrence relation:
-
tableseq takes three arguments:
-
f(x), a formula which defines the recurrence, through un+1=f(un).
- x, the variable.
- u0, the initial term of the sequence.
- tableseq(f(x),x,u0) fills the current column of the
spreadsheet, starting with the selected cell (or cell 0 if the entire
column is selected), with the formula f(x), the next cell with the
variable x, followed by the terms u0, u1, … of the
sequence. (If the current cell is column C, row n, these latter
cells will actually contain (if in row k)
=evalf(subst(C$n,C$(n+1),C(k−1))), which means if
you change the value in one cell, the values in the later cells will
change accordingly.) See also plotseq,
Section 8.17, for a graphic representation of a one-term
recurrence sequence.
Example.
Display the values of the sequence u0=3.5, un+1=sin(un)
Select a cell of the spreadsheet (for example B0) and
input in the command line:
tableseq(sin(x),x,3.5)
Output:
row | B |
0 | sin(x) |
1 | x |
2 | 3.5 |
3 | -0.35078322769 |
4 | -0.343633444925 |
5 | -0.336910330426 |
… | … |
More generally, for a recurrence relation where each term depends on
the previous k terms:
-
tableseq takes three arguments:
-
f(x1,x2,…,xk), a formula which defines the
recurrence, through un+1=f(un,…,un−k).
- [x1,…,xk], a list of variables.
- [u0,…,uk−1], a list of the beginning k terms.
- tableseq(f(x1,…,xk),[x1,…,xk],[u0,…,uk−1])
fills the current column of the
spreadsheet, starting with the selected cell (or cell 0 if the entire
column is selected), with the formula f(x1,x2,…,xk),
followed by the variables x1,…,xk, followed by the
terms u0, u1, … of the sequence.
Example.
Display the values of the Fibonacci sequence
u0=1, u1=1,…, un+2=un+un+1
Select a cell, say B0, and:
Input:
tableseq(x+y,[x,y],[1,1])
Output:
row | B |
0 | x+y |
1 | x |
2 | y |
3 | 1 |
4 | 1 |
5 | 2 |
… | … |