General resources:

• Mathematics ArXive
• On-line Encyclopedia of Integer Sequences
• Math 192 stuff
• Jim Propp articles

Applets:

• Tiling Applets
• Toad Shuffle Applet

Grove-related stuff:

• Gabriel D. Carroll, David Speyer, The Cube Recurrence
• Eric H. Kuo, Applications of Graphical Condensation for Enumerating (condensation)
• David Speyer's article on how the octahedron recurrence counts matchings of crosses and wrenches graphs is on his site off of the private REACH site.

Trihex-related stuff:

• Jim Propp, A Pedestrian Approach to a Method of Conway, or, A Tale of Two Cities (skew).
• Other articles listed at http://www.ens-lyon.fr/~eremila/ may also be of interest.
• For information about solving the word-problem in discrete groups that
  have a geometrical nature, see
          http://www.geom.umn.edu/docs/forum/automaticgroups/
  If this whets your appetite, check out the book "Word Processing in Groups"
  by D.B.A. Epstein, J.W. Cannon, D.F. Holt, S.V.F. Levy, M.S. Paterson, and
  W.P. Thurston (Jones and Bartlett Publishers, Boston, 1992).
  

Domino-related stuff:

• Dimers and Dominoes (domino), which demonstrates Kasteleyn method.
• Trees and Matchings applications of the Kasteleyn method and of the matrix-tree method, both of which involve discrete Fourier theory on graphs.  One of these examples has interesting 3-adic properties.
• Other articles at Rick Kenyon's web-site http://topo.math.u-psud.fr/~kenyon/papers/papers.html may also be of interest, including

        C. Kenyon and R. Kenyon,
        Tiling a polygon with rectangles,
        Proc. of 33rd Fundamentals of Computer Science (FOCS), (1992):610-619.
In this article, the Kenyons give an algorithm which tiles a simple polygon with 1Xn and mX1 bars, or decides that one does not exist.  A consequence is that the space of tilings is connected by simple local transformations.  The proof uses an analysis of the Conway tiling group.
• A paper by Lior Pachter on the form of N(n).
• A paper by Henry Cohn on the 2-adic continuity of N(n).

Assigned papers:

• Jim Propp, A reciprocity theorem for domino tilings
• Jim Propp,  /bilinear/domino