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 A271104 Number of magic and semi-magic tori of order n composed of the numbers from 1 to n^2. 3
 1, 0, 1, 4293, 23161722048, 2627518340149999905600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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). 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. LINKS Dwane Campbell, Analysis of order-4 magic squares, (2013). Dwane Campbell, Order-4 squares grouped by base square quartets, (2013). Dwane Campbell, Features in order-4 magic squares, (2013). William Walkington, 255 tores magiques d'ordre 4, et 1 tore magique d'ordre 3, (2011). William Walkington, Passage du carrĂ© au tore magique, (2011). William Walkington, 255 fourth-order magic tori, and 1 third-order magic torus, (2012). William Walkington, From the magic square to the magic torus, (2012). William Walkington, (using findings computed by Walter Trump), 251 449 712 fifth-order magic tori, (2012). William Walkington, A new census of fourth-order magic squares, (2012). William Walkington, Table of fourth-order magic tori, (2012). FORMULA a(n) = A271103(n)/ n^2. CROSSREFS Cf. A006052, A270876, A271103. Sequence in context: A204408 A204401 A204400 * A234164 A124596 A224522 Adjacent sequences:  A271101 A271102 A271103 * A271105 A271106 A271107 KEYWORD nonn,more AUTHOR William Walkington, Mar 30 2016 EXTENSIONS a(6) added by William Walkington, Jul 18 2018 STATUS approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)