A271104 Number of magic and semi-magic tori of order n composed of the numbers from 1 to n^2.

1, 0, 1, 4293, 23161722048, 2627518340149999905600

Offset: 1

Author

William Walkington, Mar 30 2016

Keywords

• nonn
• more

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 carré 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).

Crossrefs

Cf. A006052, A270876, A271103.

Formula

a(n) = A271103(n)/ n^2.

Extensions

a(6) added by William Walkington, Jul 18 2018