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%I #36 Jan 07 2020 11:46:02
%S 1,0,1,4293,23161722048,2627518340149999905600
%N Number of magic and semi-magic tori of order n composed of the numbers from 1 to n^2.
%C Initially based on empirical observations by the author, the results for the magic tori of orders 1 to 4, have since been computed and confirmed by _Walter Trump_. The results for the magic tori of order 5, and for the semi-magic tori of orders 4 and 5, have been computed by _Walter Trump_. The result for the order 6 is deduced from Artem Ripatti's findings (cf. A271103).
%C A semi-magic torus differs from a magic torus in that there are no magic intersections of magic diagonals, and in consequence only semi-magic squares are displayed on its surface.
%H Dwane Campbell, <a href="http://magictesseract.com/order-4_squares">Analysis of order-4 magic squares</a>, (2013).
%H Dwane Campbell, <a href="http://magictesseract.com/Frenicle_squares">Order-4 squares grouped by base square quartets</a>, (2013).
%H Dwane Campbell, <a href="http://magictesseract.com/order-4_features">Features in order-4 magic squares</a>, (2013).
%H William Walkington, <a href="http://carresmagiques.blogspot.fr/2011/10/255-tores-magiques-dordre-4-et-1-tore.html">255 tores magiques d'ordre 4, et 1 tore magique d'ordre 3</a>, (2011).
%H William Walkington, <a href="http://carresmagiques.blogspot.fr/2011/11/passage-du-carre-au-tore-magique.html">Passage du carré au tore magique</a>, (2011).
%H William Walkington, <a href="http://carresmagiques.blogspot.fr/2012/01/255-fourth-order-magic-tori-and-1-third.html">255 fourth-order magic tori, and 1 third-order magic torus</a>, (2012).
%H William Walkington, <a href="http://carresmagiques.blogspot.fr/2012/03/from-magic-square-to-magic-torus.html">From the magic square to the magic torus</a>, (2012).
%H William Walkington, (using findings computed by _Walter Trump_), <a href="http://carresmagiques.blogspot.fr/2012/09/251-449-712-fifth-order-magic-tori.html">251 449 712 fifth-order magic tori</a>, (2012).
%H William Walkington, <a href="http://carresmagiques.blogspot.fr/2012/04/a-new-census-of-fourth-order-magic.html">A new census of fourth-order magic squares</a>, (2012).
%H William Walkington, <a href="http://carresmagiques.blogspot.fr/2012/10/table-of-fourth-order-magic-tori.html">Table of fourth-order magic tori</a>, (2012).
%F a(n) = A271103(n)/ n^2.
%Y Cf. A006052, A270876, A271103.
%K nonn,more
%O 1,4
%A _William Walkington_, Mar 30 2016
%E a(6) added by _William Walkington_, Jul 18 2018
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