Table of values and graph of a recurrent sequence : tableseq and plotseq

tableseq is a command that should be used inside a spreadsheet (opened with Alt+t), it returns a template to fill one column with $\tt u_0, \ u_{n+1}=f(u_{n})$ (one-term recurrence) or more generally u₀,..., u_k,  u_n+k+1 = f (u_n, u_n+1,..., u_n+k). The template fills the column starting from the selected cell, or starting from 0 if the whole column was selected.
See also plotseq (section 2.13) for a graphic representation of a one-term recurrence sequence.

Examples :

• display the values of the sequence u₀ = 3.5, u_n = sin(u_n-1)
  Select a cell of the spreadsheet (for example B0) and input in the command line :
  tableseq(sin(n),n,3.5)
  Output :
  a column with sin(n), n, 3.5 and the formula evalf(subst(B$0,B$1,B2))
  You get the values of the sequence $\tt u_0=3.5,\ u_n=sin(u_{n-1})$ in the column B.
• display the values of the Fibonacci sequence u₀ = 1, u₁ = 1 u_n+2 = u_n + u_n+1
  Select a cell, say B0, and input in the command line
  tableseq(x+y,[x,y],[1,1])
  This fills the B column sheet with

  row	B
  0	x+y
  1	x
  2	y
  3	1
  4	1
  5	2
  ..	..
  7	5
  ..	..