1. ## Mathematica and Sequences

I have the following code, but I dont know why I could not make it work :S
Code:
x = Table[1, {i, 1, 15}];
For[i = 3, i < 15, i++,
x[i + 1] = 16/9*x[i] - 2/3*x[i - 1] - 1/3*x[i - 2]
]
Graphics[Point[Table[{i, x[i]}, {i, 1, 15}]]]

2. Need double brackets in an array : x[[i]]. The syntax x[i] is interpreted as the function x at the value i.

3. Originally Posted by shawsend
Need double brackets in an array : x[[i]]. The syntax x[i] is interpreted as the function x at the value i.

Code:
s = 12;
x = Table[1, {i, 1, s}];
For[i = 3, i <= s - 1, i++,
x[[i + 1]] = 16/9*x[[i]] - 2/3*x[[i - 1]] - 1/3*x[[i - 2]];
]
Graphics[Point[Table[{i, x[[i]]}, {i, 1, s, 1}]]]

4. I again have problems about scaling the graphic :S

Code:
s = 50;
x = Table[1, {i, 1, s}];
xmin := 1;
xmax := 1;
For[i = 3, i <= s - 1, i++,
c = 16/9*x[[i]] - 2/3*x[[i - 1]] - 1/3*x[[i - 2]];
x[[i + 1]] := c;
xmin = If[c < xmin, c, xmin];
xmax = If[c > xmax, c, xmax];
]
Graphics[Point[Table[{i, x[[i]]}, {i, 1, s, 1}]], Axes -> True]
I found out that the following code is more useful:
Code:
s = 50;
x = Table[1, {i, 1, s}];
For[i = 3, i <= s - 1, i++, x[[i + 1]] = 16/9*x[[i]] - 2/3*x[[i - 1]] - 1/3*x[[i - 2]] ]
ListPlot[Table[{i, x[[i]]}, {i, 1, s}]]