Explicit Polynomial Expressions for the Enumeration of 3 by 4 and 3 by 5 Semi-Magic Rectangles

Explicit Polynomial Expressions for the Enumeration of 3 by 4 and 3 by 5 Semi-Magic Rectangles
By Shalosh B. Ekhad and StudentsOfDrZ ExpMathClass
.txt [only .txt format]

Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
Posted: Feb. 26, 2019
StudentsOfDrZ ExpMathClass:= { Yonah Biers-Ariel, Victoria Chayes, Tong Cheng, Terence Coelho ,Quentin Dubrorff ,Matthew Hohertz, Jingze Li, Joseph Olsen, Jason Saied, Lauren Squillace, Yukun Yao, Tianhao Zhang, Songhao Zhu}

The number of n by n semi-magic, where all the row- and column-sums add up to r, is famously a polynomial of degree (n-1)^2 in r, with certain nice properties, thanks to a famous theorem of Richard Stanley and Eugene Ehrhart.
But what about semi-magic rectangles? Now the polynomials are not so nice, but using Experimental Mathematics, and automated guessing, one can derive explicit formulas.
This article was derived during Doron Zeilberger's Eperimental Mathematics Class (Spring 2019) , in Class 6 (Feb. 11, 2019).

Maple package

MagicRectangles.txt, a Maple package to compute explicit polynomial expressions for the number of semi-magic rectangles

Input and Output for MagicRectangles.txt

If you want to see the input file that generated this article
the input file generates the output file.

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