How to exclude categories from home?

I’m trying to exclude certain categories from home. Whatever i tried does not work, can anyone give me a hint please?
Here is the code:

<?php
$posts = query_posts($query_string . '&posts_per_page=20');
while ( have_posts() ) : the_post() ?>

<div class="thumbnail">

<h2 style="margin:0px; padding:0px">
<?php
$category = get_the_category();
echo $category[0]->cat_name;
?>
</h2>

<div id="post-<?php the_ID() ?>" class="<?php sandbox_post_class() ?>">

<h3 class="entry-title" style="margin-top:0px; padding-top:0px">
<div class="floatright" style="padding:0px">
<?php the_post_thumbnail( 'thumbnail' ); ?>
</div>

<a href="<?php the_permalink() ?>" title="<?php printf( __('Permalink to %s', 'sandbox'), the_title_attribute('echo=0') ) ?>" rel="bookmark"><?php the_title() ?></a></h3>

I’ve tried this (does not work):

$cats_to_exclude = array(

69, // Call for entries

16, // Competitions

70, // Meetings & talks

71, // Exhibitions

72, // Workshops

);

Any better ideas? Very grateful!