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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
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, Features in order-4 magic squares, (2013).
William Walkington, Passage du carré au tore magique, (2011).
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
KEYWORD
nonn,more
AUTHOR
William Walkington, Mar 30 2016
EXTENSIONS
a(6) added by William Walkington, Jul 18 2018
STATUS
approved