TofZ

TofZ.php

<?php
/**
 * Created by PhpStorm.
 * User: kayladnls
 * Date: 12/13/14
 * Time: 7:24 PM
 */

// Bt(z)^r == sigma(k) * (tk + r, k) * r / tk + r * z^k
// Problem: Compute the number of 4th order ternary trees;
// t = 3; k = 4;, r = 1

// Binomial coefficients (tk + r, k) is computed
// n!/(n-k)!k!

$t = 3;
$r = 1;
$k = 4;
$string_answer = "1 +";

$arr = array_fill(0, $k, 0);


foreach ($arr as $idx => $value)
{
    $i = $idx + 1;
    $n1 = ($t*$i) + $r;
    $n2 = $i;

    $bc = binomialCoefficient($n1, $n2);
    $answer = $bc * ($r/(($t*$i) +$r));

    $string_answer .= strval($answer)."z^".$i." + ";
}

echo trim($string_answer, '+');

function binomialCoefficient($num1, $num2)
{
    return factorial($num1) / (factorial(($num1 - $num2)) * factorial($num2));
}

function factorial($n)
{
    $answer = $n;
    while ($n > 1)
    {
        $answer *= ($n-1);
        $n--;
    }

    return $answer;
}