A174021 Number of symmetry classes of reduced 3x3 magilatin squares with magic sum n.

1, 1, 2, 3, 6, 8, 16, 15, 25, 30, 41, 43, 66, 68, 92, 99, 129, 136, 180, 180, 231, 245, 297, 304, 385, 388, 469, 482, 575, 588, 706, 704, 831, 858, 987, 996, 1171, 1175, 1350, 1370, 1561, 1581, 1806, 1804, 2047, 2081, 2323, 2335, 2641, 2649, 2951, 2979, 3302

Offset

3,3

Comments

A magilatin square has equal row and column sums and no number repeated in any row or column. It is reduced if the least value in it is 0. The symmetries are row and column permutations and diagonal flip.

a(n) is given by a quasipolynomial of degree 4 and period 840.

References

Matthias Beck and Thomas Zaslavsky, An enumerative geometry for magic and magilatin labellings, Annals of Combinatorics, 10 (2006), no. 4, pages 395-413. MR 2007m:05010. Zbl 1116.05071.

Links

Thomas Zaslavsky, Table of n, a(n) for n=3..10000.

Matthias Beck and Thomas Zaslavsky, Six Little Squares and How Their Numbers Grow , J. Int. Seq. 13 (2010), 10.6.2.

Matthias Beck and Thomas Zaslavsky, "Six Little Squares and How their Numbers Grow" Web Site: Maple worksheets and supporting documentation.

Index entries for linear recurrences with constant coefficients, signature (-2, -3, -3, -2, 0, 3, 6, 9, 10, 9, 5, 0, -6, -11, -14, -14, -11, -6, 0, 5, 9, 10, 9, 6, 3, 0, -2, -3, -3, -2, -1).

Crossrefs

Cf. A173549 (all magilatin squares), A173730 (symmetry types), A174020 (reduced squares), A174019 (reduced symmetry types by largest value).

Sequence in context: A300671 A268645 A047001 * A267007 A091070 A133586

Adjacent sequences: A174018 A174019 A174020 * A174022 A174023 A174024

Keyword

nonn

Author

Thomas Zaslavsky, Mar 05 2010

Extensions

"Distinct" values (incorrect) deleted by Thomas Zaslavsky, Apr 24 2010

Status

approved