Séminaire Lotharingien de Combinatoire, B66a (2011), 27 pp.
Alin Bostan, Frédéric Chyzak, Mark van Hoeij and
Explicit Formula for the Generating Series of Diagonal 3D Rook Paths
Let an denote the number of ways in which a chess rook can move from a
corner cell to the opposite corner cell of an n x n x n
three-dimensional chessboard, assuming that the piece moves closer to the goal
cell at each step. We describe the computer-driven
proof of the fact that the generating series
admits the following explicit expression in terms of a Gaussian hypergeometric function:
Received: May 18, 2011.
Accepted: July 7, 2011.
Final Version: October 4, 2011.
The following versions are available: