A056840

[David Wasserman]

Dear Joseph S. Myers,
     Thanks.  I've checked that there are 99 spanning trees of 
5-plets, and that each appears once in the picture.  For 6-plets, I 
haven't tried to count all of them, but I have tried to count all the 
ones with multiple spanning trees.  I've found 23 (pictured below), 
with a total of 76 trees.  This isn't quite enough to account for the 
difference A056840(6) - A030222(6) = 56.  Have I missed any?

  - David


XXX
  X X		3 spanning trees
   X

   X
XX X		3 spanning trees
  XX

XX
X XX		3
  X
 
    X
XXX X	 2
    X

   X
XX X   4
X X

XX      XX      XX
X X     X X     X X   3 each
  X       X     X X
    X    X

X
  XX
  X X   2
   X

  X
X XX  3
  X
  X

   X           X          X         X
XX X        XX X       XX X      XX X    4 each
   X           X          X X    X  X
  X             X

  X
X X         4
  X X
    X

  X
X X
  X X    6
   X

  X X       X X     X X X
X X       X X       X X  2 each
  X X     X X         X

     X
  X X     X X      X X
X X     X X X    X X     4 each
  X       X        X
                    X
  X X
X X      3
  X
X