This is a very simple question but I couldn't find it in the documentation; if it's there, kindly point it out.

I want to define a Recurrence Table for the iteration x[n+1]=a*x[n] + E[n], where E[n] is a series of numbers I've entered separately {E[1],E[2],...}. What is the syntax for doing this? (i.e, once the rest of RecurrenceTable command is included - initial condition, etc.)

  • $\begingroup$ I'm not sure what's bothering you. You can do exactly what you've written, for example: e[1]=1;e[2]=3;e[3]=10; RecurrenceTable[a[n+1]==2a[n]+e[n]&&a[1]==0,a[n],{n,1,4}]. $\endgroup$
    – Domen
    Commented Jun 24 at 22:24
  • $\begingroup$ Thanks for your reply. I have a list of about 35 numbers; do I have to write them this way one-by-one or can I enter them a a list and have RecurrenceTable read from that? $\endgroup$
    – Alan
    Commented Jun 24 at 23:16
  • $\begingroup$ You could do what @ydd showed below, or something like: eVals = {1, 3, 10}; e[n_?NumericQ] := eVals[[n]]; $\endgroup$
    – Domen
    Commented Jun 25 at 14:20

1 Answer 1


One possibility is to use FoldList. As a short symbolic example:

eList = Array[e, 3];
FoldList[a #1 + #2 &, x[1], eList]

![enter image description here

Or if you prefer a numeric example:

eList = Range[3];
a = 2;
x[1] = 0;
FoldList[a #1 + #2 &, x[1], eList]

(*{0, 1, 4, 11}*)

Another option (though I have a feeling this could be a dangerous idea for some reason) is to MapThread Set across a range of e[i] for some given values and use RecurrenceTable:

eList = Array[e, 3];
eVals = Range[3];
MapThread[Set, {eList, eVals}];
RecurrenceTable[x[n + 1] == 2 x[n] + e[n] && x[1] == 0, 
 x[n], {n, 1, 4}]
(* {0, 1, 4, 11} *)


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