Sequence 1, 2, 4, 12

Hi everyone!

I need to know the rule for generating the following sequence: 1, 2, 4, 12 (that's all, no more values in the sequence). Does anyone have an idea for the rule to go forward (1-->2-->4-->12) and backward (12-->4-->2-->1)?

Any help is really apreciated! Thanks in advance.

Answer 1

[Matt J]

One possibility:

p=[0.833333333333333  -4.499999999999996   8.666666666666661  -3.999999999999996];

polyval(p,1:4)

ans = 1×4

1.0000 2.0000 4.0000 12.0000

polyval(p,4:-1:1)

ans = 1×4

12.0000 4.0000 2.0000 1.0000

Answer 2

[Hernia Baby]

You can use polyfit and polyval.

Here is one of examples.

n = 6;
x = 1:4;
y = [1,2,4,12];
p = polyfit(x,y,n)

Warning: Polynomial is not unique; degree >= number of data points.

p = 1×7

0.0098 -0.0438 0 0.2487 0 0 0.7853

x1 = linspace(0,4,100);
y1 = polyval(p,x1);

figure
plot(x,y,'o')
hold on
plot(x1,y1)
hold off