Hexagonal Nurikabe

Nurikabe is a popular grid puzzle, usually played on a square grid. Here is my attempt to adapt it to a hexagonal grid.
To solve it, you must shade cells in the grid such that these conditions are met:

• Like regular Nurikabe, each region of unshaded cells must contain exactly one number, which is equal to the size of the region. (numbered cells can never be shaded)
• All shaded cells must form a continuous region
• Three shaded cells must not form a closed triangle (i.e. Three cells around a vertex must not all be shaded)

Here it is in text form if you prefer

             __
          __/  __
       __/ 2__/  __
    __/  __/  __/  __
 __/  __/  __/  __/  __
/  __/  __/ 2__/  __/ 4
__/ 1__/  __/  __/  __/
/  __/  __/  __/  __/  
__/  __/  __/  __/  __/
/  __/  __/  __/  __/  
__/  __/  __/  __/  __/
/  __/  __/  __/  __/  
__/ 3__/  __/13__/  __/
/  __/  __/  __/  __/  
__/  __/  __/  __/ 7__/
   __/  __/  __/  __/
      __/  __/  __/
         __/  __/
            __/