LayoutManager for RecyclerView Grid with different cell width

You can use StaggeredGridLayoutManager.LayoutParams to change width and height of cells, What you expect to design follows a simple pattern, If you assign every cell an index (in the order that StaggeredGridLayoutManager arranges them by default) you will have this:

index % 4 == 3           --->  full span cell
index % 8 == 0, 5        --->  half span cell
index % 8 == 1, 2, 4, 6  ---> quarter span cell

first declare some constants in adapter to define span types:

private static final int TYPE_FULL = 0;
private static final int TYPE_HALF = 1;
private static final int TYPE_QUARTER = 2;

Then override getItemViewType method in your adapter like this:

@Override
public int getItemViewType(int position) {
    final int modeEight = position % 8;
    switch (modeEight) {
        case 0:
        case 5:
            return TYPE_HALF;
        case 1:
        case 2:
        case 4:
        case 6:
            return TYPE_QUARTER;
    }
    return TYPE_FULL;
}

All you need to do is change layoutparams considering viewType of the holder:

@Override
public MyHolder onCreateViewHolder(final ViewGroup parent, final int viewType) {
    final View itemView =
            LayoutInflater.from(mContext).inflate(R.layout.items, parent, false);
    itemView.getViewTreeObserver().addOnPreDrawListener(new ViewTreeObserver.OnPreDrawListener() {
        @Override
        public boolean onPreDraw() {
            final int type = viewType;
            final ViewGroup.LayoutParams lp = itemView.getLayoutParams();
            if (lp instanceof StaggeredGridLayoutManager.LayoutParams) {
                StaggeredGridLayoutManager.LayoutParams sglp =
                        (StaggeredGridLayoutManager.LayoutParams) lp;
                switch (type) {
                    case TYPE_FULL:
                        sglp.setFullSpan(true);
                        break;
                    case TYPE_HALF:
                        sglp.setFullSpan(false);
                        sglp.width = itemView.getWidth() / 2;
                        break;
                    case TYPE_QUARTER:
                        sglp.setFullSpan(false);
                        sglp.width = itemView.getWidth() / 2;
                        sglp.height = itemView.getHeight() / 2;
                        break;
                }
                itemView.setLayoutParams(sglp);
                final StaggeredGridLayoutManager lm =
                        (StaggeredGridLayoutManager) ((RecyclerView) parent).getLayoutManager();
                lm.invalidateSpanAssignments();
            }
            itemView.getViewTreeObserver().removeOnPreDrawListener(this);
            return true;
        }
    });

    MyHolder holder = new MyHolder(itemView);
    return holder;
}

My adapter always returns 50 for items count(just a test) and I used a simple layout file for items, It contains a LinearLayout and a TextView to show the position of holder, Remember you should pass 2 for spanCount (int the StaggeredGridLayoutManager constructor) because of your design.

@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_main);
    RecyclerView rv = (RecyclerView) findViewById(R.id.rv);
    StaggeredGridLayoutManager lm =
            new StaggeredGridLayoutManager(2, StaggeredGridLayoutManager.VERTICAL);
    rv.setLayoutManager(lm);
    rv.setAdapter(new MyAdapter(this));

}

PS:
For lazy people like me maybe it’s a simpler way rather than extending my custom LayoutManager, But I’m sure there are better ways to achieve this.

Update:
Updated part of your question is more simpler, You can use GridLayoutManager:

    GridLayoutManager glm = new GridLayoutManager(this, 3);
    glm.setSpanSizeLookup(new GridLayoutManager.SpanSizeLookup() {
        @Override
        public int getSpanSize(int position) {
            if (position % 3 == 2) {
                return 3;
            }
            switch (position % 4) {
                case 1:
                case 3:
                    return 1;
                case 0:
                case 2:
                    return 2;
                default:
                    //never gonna happen
                    return  -1 ;
            }
        }
    });
    rv.setLayoutManager(glm);

In this way you set 3 for default span size, Then considering the position of your span, Each item occupies 1, 2 or 3 spans, Something like this:

Item0.width == 2 X Item1.width
Item2.width == 3 X Item1.width
Item0.width == 2/3 X Item1.width