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Séminaire Lotharingien de Combinatoire, B66a (2011), 27 pp.

# Alin Bostan, Frédéric Chyzak, Mark van Hoeij and
Lucien Pech

# Explicit Formula for the Generating Series of Diagonal 3D Rook Paths

**Abstract.**
Let *a*_{n} 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
*discovery and
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: