Here's a different method that doesn't use tiled clones at all, just for the hell of it.
Before you begin enable the following snapping options: Snapping, Snap nodes paths and handles, Snap cusp nodes inc. rectangles. This will help you place everything accurately.
Draw a hexagon with a stroke anand no fill, copy and paste it, and move so that they both intersect.
Continue pasting intersecting hexagons until you have this complete shape, select all, and do Path > Combine
Copy and paste to get a complete column of shapes, then delete the four in the middle indicated by the dotted line, leaving the two end copies (4 and 5)
This is the original shape
Add a thicker stroke to this shape
Select both shapes 4 and 5, and do a four step interpolation using Extensions > Generate from path > Interpolate, and make sure you enable the Interpolate Styles option.
Copy and paste additional columns, moving and snapping into place until you have the complete pattern
This is the complete graphic. Strokes set to white, under that a copy with strokes set to black and a blur added and moved slightly to offset the shadow, and under that a filled rectangle. All are grouped and then clipped using a rectangle drawn on top as a clipping path.