       Recursive function

• To: mathgroup at smc.vnet.net
• Subject: [mg115898] Recursive function
• From: StatsMath <stats.math8 at gmail.com>
• Date: Tue, 25 Jan 2011 04:20:19 -0500 (EST)

```I am trying to compute the following function:

x[t] = a * x[t-1] + b * x[t-2]
x = 1
x = 1

For different values of a & b.

Would like to use Manipulate[] so that I can change the values of a &
b dynamically and observe what the resulting x[t] values are.

So wrote the following piece of code:

Clear["Global`*"]
x[t_Integer] := x[t] = a x[t - 1] + b x[t - 2]
x = 1;
x = 1;
Manipulate[Map[x[#] &, Range[0, 3]], {a, -1, 1, 0.5}, {b, -1, 1, .5}]

Got the following results:
{1, 1, a + b, b + a (a + b)}

The a & b values are not being propagated so tried the following:

Clear["Global`*"]
x[t_Integer] := x[t] = a x[t - 1] + b x[t - 2] /; t > 2
x = 1;
x = 1;
Manipulate[
Map[(If[# == 0 || # == 1, 1, a x[# - 1] + b x[# - 2]]) &,
Range[0, 3]], {a, -1, 1, 0.5}, {b, -1, 1, .5}]

Got the following result:
{1, 1, -2, -1 - a - b}

Finally got it working with the following code:

Clear["Global`*"]
Manipulate[
Map[(If[# == 0 || # == 1, x[#] = 1,
x[#] = a x[# - 1] + b x[# - 2]]) &, Range[0, 20]], {a, -1, 1,
0.5}, {b, -1, 1, .5}]

The above code looks ugly, so wondering if there is a different way to
handle recursive functions.

Thanks!

```

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