fcalc

#!/usr/bin/perl

#use warnings;
use strict;
use Getopt::Long;
use fralib;
use POSIX qw(ceil floor);
use File::Path;
use Pod::Usage;

for my $n (0..200)
{
	
	my $a = ncr(2*$n, $n);
	my $b = 0;
	
	for my $x (0..$n)
	{
		my $j = ncr($n, $x);
		$b += $j*$j;
	}
	
	print "$n)$a\t$b\n";
	
}

exit;


print "ncr(3,1) = " . ncr(3,1) . "\n";
print "ncr(10,1) = " . ncr(10,1) . "\n";
print "ncr(10,9) = " . ncr(10,9) . "\n";
print "ncr(-3,1) = " . ncr(-3,1) . "\n";

my $p = 1/90;
my $q = 1- $p;
my $n = 60;

my $a = 0;

for my $k (0..4)
{
	$a += ncr($n,$k)*$p**$k*$q**($n-$k);
}

my $gte5 = 1-$a;
my $newyork = 5 * 62 * $gte5;
my $USA = 10 * 50 * 5 * 62 * $gte5;

print <<STUFF;
<5       : $a
>=5      : $gte5
new york : $newyork
usa      : $USA

STUFF

sub ncr
{
	my ($n, $r) = @_;
	
	if ($r==0)
	{
		return 1;
	}
	elsif ($n<=0)
	{
		return 0;
	}
	elsif ($r<0)
	{
		return 0;
	}
	elsif ($r>$n)
	{
		return 0;
	}
	elsif ($r > $n-$r)
	{
		return ncr($n,$n-$r);		
	}
	else
	{
		return ($n/$r) * ncr($n-1, $r-1);
	}
}