

A271104


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


3




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 semimagic 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 semimagic torus differs from a magic torus in that there are no magic intersections of magic diagonals, and in consequence only semimagic squares are displayed on its surface.


LINKS

Table of n, a(n) for n=1..6.
Dwane Campbell, Analysis of order4 magic squares, (2013).
Dwane Campbell, Order4 squares grouped by base square quartets, (2013).
Dwane Campbell, Features in order4 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 fourthorder magic tori, and 1 thirdorder 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 fifthorder magic tori, (2012).
William Walkington, A new census of fourthorder magic squares, (2012).
William Walkington, Table of fourthorder 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



