RecurrenceTable with vector

Question

Mathematica can do a RecurrenceTable with a vector, here is a simple example:

RecurrenceTable[{x[n + 1] == 2* x[n], x[0] == {1, 2, 3}}, x, {n,  3}]

with output

{{1, 2, 3}, {2, 4, 6}, {4, 8, 12}, {8, 16, 24}}

I want to do something similar but instead of multiplying by 2 I want to multiple each element in x[n] by a different number. For example, one would think that this would work:

RecurrenceTable[{x[n + 1] == {1,2,3}* x[n], x[0] == {1, 2, 3}}, x, {n,  3}]

since Times is listable but I get an error

RecurrenceTable::excptn: Value {1,2,3,2,4,6,3,6,9} is a numerical exception. >>

I get the same result using MapThread etc. Thoughts?

Answer 1

The trick below seems to work in this simple case :

g[input_List] := {1, 2, 3} input 

RecurrenceTable[{x[n + 1] == g[x[n]], x[0] == {1, 2, 3}}, x, {n, 3}]
(* {{1, 2, 3}, {1, 4, 9}, {1, 8, 27}, {1, 16, 81}} *)