Geometric progression?

[iCeR]

Hi,

 

I'm working on a referral system - the formula is exactly like the pyramid/ponzi scheme.

 

The system works like this:

 

The initial user signs up (tier 1)

The initial user refers 3 friends (tier 2)

Each of those 3 friends refer another 3, (tier3)

etc.

 

What would be the mathematical formula for that? (I think it's called geometric progression)

 

How could I code up something in PHP where I could enter a number and it will then give me the number of tiers it has gone down and a semi-visual.

 

ie: I enter 13 - it displays the text "3 tiers" and then displays

 

     o
     |
    ooo
   / | \
ooooooooo

[sasa]

<?php
$number = 41;
echo $d = ceil(log(2*$number)/log(3))," tiers<br />\n";
$x = 1;
for($i = 1; $i<$d;$i++){
    echo str_repeat('o', $x),"<br />\n";
    $number -= $x;
    $x *= 3;
}
echo str_repeat('o', $number),"<br />\n";
?>

[iCeR]

Perfect! Thanks Sasa