Wordpress category posts with pagenation in page template - wordpress

Question

I'm using the code below to display in a custom page, a list with posts from a certain category. I would like to add pagenation at the bottom, but until now, I fail.
Any way to add it somehow?
<?php $cat_id = 22;
$cat_link = get_category_link( $cat_id );
$cat_name = get_cat_name($cat_id); ?>
<div class="catrecent">
<?php $query = new wp_query();
$query->query('showposts=1&cat=' . $cat_id);
if ($query->have_posts()) : while ($query->have_posts()) : $query->the_post(); ?>
<div class="recenttitle">
<h2 class="catidtxt"> <?php echo ($cat_name); ?></h2>
<h2 class="recentposttitle"><?php the_title(); ?></h3>
</div>
<div class="recentpostwrap">
<?php the_post_thumbnail( 'catlarge' ); ?>
<?php the_content_limit(600,""); ?>
</div>
<?php endwhile; else: ?><?php endif; ?><?php wp_reset_query(); ?>
</div>
<ul class="posts_list">
<?php $query = new wp_query();
$query->query('offset=1&showposts=4&cat=22&paged=' . $cat_id);
if ($query->have_posts()) : while ($query->have_posts()) : $query->the_post(); ?>
<li>
<?php the_post_thumbnail( 'catmed' ); ?>
<?php the_title(); ?>
</li>
<?php endwhile; else: ?><?php endif; ?><?php wp_reset_query(); ?>
</ul>

Answer 1

Useful links: http://codex.wordpress.org/Function_Reference/paginate_links, http://codex.wordpress.org/Making_Custom_Queries_using_Offset_and_Pagination
Try something like this
<ul class="posts_list">
<?php
$paged = ( get_query_var( 'paged' ) ) ? get_query_var( 'paged' ) : 1;
$ppp = 4;
$offset = 1;
//Manually determine page query offset (offset + current page (minus one) x posts per page)
$page_offset = $offset + ( ($paged - 1) * $ppp );
$query = new wp_query(array(
'offset' => $page_offset,
'posts_per_page' => $ppp,
'cat' => $cat_id,
'paged' => $paged
));
if ($query->have_posts()) : while ($query->have_posts()) : $query->the_post(); ?>
<li>
<?php the_post_thumbnail( 'catmed' ); ?>
<?php the_title(); ?>
</li>
<?php endwhile; else: ?><?php endif; ?>
</ul>
<?php
// pagination
$big = 999999999; // need an unlikely integer
echo paginate_links(array(
'base' => str_replace( $big, '%#%', esc_url( get_pagenum_link( $big ) ) ),
'total' => ceil(($query->found_posts - $offset) / $ppp),
'format' => '?paged=%#%',
'current' => max( 1, get_query_var('paged') ),
));
wp_reset_query();
?>