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I wrote a fifteen puzzle simulation back in 2010 which I recently went back to and updated before submitting it as freeware to the Apple App Store.

Playing around, I then plugged my model into my coset solver framework and performed a states at depth enumeration in the multi-tile metric out to depth 23:

XV Puzzle Enumerator Client(bdm.local)

XV Coset Solver
	Fixed tokens in subgroup: 0, 1, 2, 3, 4, 8, 12, 15.
	518,918,400 cosets of size 20,160

Cosets solved since launch: 165,364,141
Average time per coset: 0:00:00.001

Server Status:
XV Puzzle Enumerator Server
Enumeration to depth: 23

Snapshot: Thursday, June 12, 2014 at 11:11:29 AM Central Daylight Time

 Depth             Reduced             Elements
   0                     1                    1 
   1                     3                    6 
   2                    11                   18 
   3                    29                   54 
   4                    87                  162 
   5                   253                  486 
   6                   752                1,457 
   7                 2,213                4,334 
   8                 6,379               12,568 
   9                18,205               36,046 
  10                51,785              102,801 
  11               145,489              289,534 
  12               405,728              808,623 
  13             1,118,586            2,231,878 
  14             3,043,537            6,076,994 
  15             8,153,139           16,288,752 
  16            21,464,200           42,897,301 
  17            55,475,870          110,898,278 
  18           140,272,410          280,452,246 
  19           346,202,190          692,243,746 
  20           831,610,844        1,662,949,961 
  21         1,938,788,875        3,877,105,392 
  22         4,370,165,315        8,739,560,829 
  23         9,490,811,983       18,980,345,944 

 Sum        17,207,737,884       34,412,307,411 

518,918,400 of 518,918,400 cosets solved