How to make pagination with different size for first page? ->paginate(X)

I think you have to code it yourself.

https://laravel.com/docs/5.7/queries#ordering-grouping-limit-and-offset : scroll down to skip / take.

@Vilfago, thanks for a hint. Here is what I ended up with as I required Paginator object and its functionality.

Basically, I make the required query outside and put in this helper function, that generates LengthAwarePaginator for me.

/**
 * Custom paginator for "load more" models excluding one element on first page.
 *
 * @param \Illuminate\Database\Eloquent\Builder $query
 * @param int $per_page
 * @return \Illuminate\Pagination\LengthAwarePaginator
 */
function getLoadMoreLengthAwarePaginator(\Illuminate\Database\Eloquent\Builder $query, $per_page = 12) {
    // query total count from DB
    $count = $query->count();

    // get a page number from request
    $page = request()->get('page') ?? 1;

    // recalculate number of items for first page
    $first_page = $per_page - 1;

    // calculate offset
    $perPage = $page == 1 ? $first_page : $per_page;
    $offset = ($page - 2) * $perPage + $first_page;

    // get a collection from DB
    $reviews = $query->skip($offset)->take($perPage)->get();

    // return Paginator instance
    return new \Illuminate\Pagination\LengthAwarePaginator(
        $reviews, $count, $per_page, $page, ['path'  => request()->url(), 'query' => request()->query()]
    );
}

Simple pagination example:

use Illuminate\Container\Container;
use Illuminate\Pagination\LengthAwarePaginator;
use Illuminate\Pagination\Paginator;

class CustomFirstPagePaginator {
    public static function simplePaginate( $query, $perFirstPage = null, $perPage = null, $columns = [ '*' ], $pageName = 'page', $page = null ) {
        $page = $page ?: Paginator::resolveCurrentPage( $pageName );

        $perPage      = $perPage ?: $query->model->getPerPage();
        $perFirstPage = $perFirstPage ?: $perPage;

        $skip        = match ( $page ) {
            1 => 0,
            default => $perFirstPage + ( $page - 2 ) * $perPage,
        };
        $realPerPage = match ( $page ) {
            1 => $perFirstPage,
            default => $perPage,
        };
        $query->skip( $skip )->take( $realPerPage + 1 );

        return Container::getInstance()->makeWith( Paginator::class, [
            'items'       => $query->get( $columns ),
            'perPage'     => $realPerPage,
            'currentPage' => $page,
            'options'     => [
                'path'         => Paginator::resolveCurrentPath(),
                'pageName'     => $pageName,
                'perPage'      => $perPage,
                'perFirstPage' => $perFirstPage,
            ],
        ] );
    }


    public static function paginate( $query, $perFirstPage = null, $perPage = null, $columns = [ '*' ], $pageName = 'page', $page = null ) {
        $page = $page ?: Paginator::resolveCurrentPage( $pageName );

        $perPage      = $perPage ?: $query->model->getPerPage();
        $perFirstPage = $perFirstPage ?: $perPage;

        $skip        = match ( $page ) {
            1 => 0,
            default => $perFirstPage + ( $page - 2 ) * $perPage,
        };
        $realPerPage = match ( $page ) {
            1 => $perFirstPage,
            default => $perPage,
        };
        $results     = ( $total = $query->toBase()->getCountForPagination() )
            ? $query->offset( $skip )->limit( $realPerPage )->get( $columns )
            : $query->model->newCollection();

        return Container::getInstance()->makeWith( LengthAwarePaginator::class, [
            'items'       => $results,
            'total'       => $total,
            'perPage'     => $realPerPage,
            'currentPage' => $page,
            'options'     => [
                'path'         => Paginator::resolveCurrentPath(),
                'pageName'     => $pageName,
                'perPage'      => $perPage,
                'perFirstPage' => $perFirstPage,
            ],
        ] );
    }
}

Then anywhere:

        $query = Article::published()->latests();

        $articles = CustomFirstPagePaginator::simplePaginate(
            $query, 7, 9
        );