Web site for the paper
“Explicit formula for the generating series of diagonal 3D rook paths”
by Alin Bostan, Frédéric Chyzak, Mark van Hoeij, and Lucien Pech

(September 2011)

All Maple code intended for Maple13.

• 3D diagonal rook sequence in Sloane's OEIS.
• 3D diagonal queen sequence in Sloane's OEIS.
• Maple code of an optimised implementation of Lipshiz's approach (Section 2.3).
• Maple code to produce the operator P and rational-function certificates S and T for the 3D rooks (Section 2.4).
• Corresponding rational-function certificates S and T. (For comparison sake, here is another set of certificates, which was obtained with an earlier piece of code: observe the different denominator structure.)
• The version of Mgfun used for the calculations above (version 4.0) is part of Algolib 13.0.
• Maple code to get the minimal-order recurrence for the 3D rooks (Section 2.5).
• Maple code to get the explicit form for the generating series (Section 2.6).
• Program equiv used in the calculation above.
• Comparison between the explicit formula obtained by creative telescoping and that obtained by the approach of Frits Beukers (Section 3.3).
• Guessed linear differential equation for the 3D queens, together with the corresponding linear recurrence equation (Section 3.4).
• Maple code to get the rectangular system for the 3D rooks (Section A.1).
• Maple code to perform the second iteration of Chyzak's algorithm for the 3D rooks (Section A.2).
• Maple code to reconstruct the final certificates from Stages A and B in the case of the 3D rooks (Section A.3).