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[0] = 1 x[1] = 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[0] = 1; x[1] = 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[0] = 1; x[1] = 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!