First three images in post excerpt

I have certain posts that are nothing but with quite a few images in them. Is there a way to define an auto generated excerpt to only display the first three images for these posts on the index, so that users would have to click through to see the rest? Thank you.

You can do this pretty easily using the do_shortcode function.

Check if an instance of exists in your post content.

Here’s a simple function to drop in functions.php that checks the current post’s content for the gallery shortcode:

function gallery_shortcode_exists(){

    global $post;

    # Check the content for an instance of  with or without arguments
    $pattern = get_shortcode_regex();
    if(
        preg_match_all( "https://wordpress.stackexchange.com/". $pattern .'/s', $post->post_content, $matches )
        && array_key_exists( 2, $matches )
        && in_array( 'gallery', $matches[2] )
    )
        return true;

    # Sourced from http://codex.wordpress.org/Function_Reference/get_shortcode_regex
}

Use do_shortcode() to render your gallery.

You can use the following within the loop in your template files:

# Determine if the post_content column contains the string 
if( gallery_shortcode_exists() ){

    # Get the first three attachments using the posts_per_page parameter
    $args = array(
        'post_type' => 'attachment',
        'post_mime_type' => 'image',
        'posts_per_page' => 3,
        'post_parent' => get_the_ID()
    );
    $attachments = get_children( $args );

    # If any attachments are returned, proceed
    if( $attachments ){

        # Spin cycle to collate attachment IDs
        foreach( $attachments as $attachment )
            $includes[] = $attachment->ID;

        # Format our IDs in a comma-delimited string
        $includes = implode(',', $includes);

        # Inject your include argument
        $shortcode = str_replace('[gallery', "[gallery include="$includes" ", get_the_content());

        # Render the Gallery using the standard editorial input syntax
        echo do_shortcode($shortcode);

        # Add a View More link
        echo '<a href="' . get_permalink() . '">' . __('View more', 'domain') . '</a>';
    }
    else
        _e('Foo Bar - No attachments found and no excerpt to display', 'domain');
}
else
    # Whatever fallback you desire
    the_excerpt();