Shadow from texture not showing up because of a transparent shader I've used a texture on a plane for this sunflower, but instead of only the diffuse part of the mix of shaders casting shadows, the transparent shader is also casting a shadow with the shape of the 2x1 plane, where as I said earlier only the flower should cast the shadow as it is a diffuse shader.
The texture is packed into the blend file.

Texture link:

http://s2.postimg.org/thhlmfi15/tilemap.png
Transparency Shadows

While the Blender Manual page says:


  For direct light sampling, use transparency of surfaces in between to produce shadows affected by transparency of those surfaces.


the tooltip is perhaps more clear:



With that option disabled, as in your case, the alpha channel of the texure won't be considered for shadows so you'll get the light occusion from the actual geometry (a plane).