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A174019 Number of symmetry classes of reduced 3 X 3 magilatin squares with largest entry n. 3
1, 2, 3, 8, 15, 24, 32, 52, 63, 94, 114, 156, 184, 244, 276, 358, 406, 504, 555, 692, 752, 910, 991, 1174, 1267, 1498, 1593, 1858, 1983, 2280, 2414, 2772, 2915, 3308, 3488, 3924, 4114, 4622, 4816, 5374, 5616, 6216, 6467, 7154, 7418, 8158, 8469, 9264, 9587 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
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 5 and period 60.
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
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, -1, 2, 5, 5, 2, -3, -7, -7, -3, 2, 5, 5, 2, -1, -2, -1).
FORMULA
G.f.: x^2/(x-1)^2 - x^3/(x-1)^3 - 2x^3/[(x-1)*(x^2-1)] - x^3/(x^3-1) - 2x^4/[(x-1)^2*(x^2-1)] - x^4/[(x-1)*(x^3-1)] - 2x^4/(x^2-1)^2 + x^5/[(x-1)^3*(x^2-1)] + x^5/[(x-1)^2*(x^3-1)] + 2x^5/[(x-1)*(x^2-1)^2] + x^5/[(x-1)*(x^4-1)] + x^5/[(x^2-1)*(x^3-1)] + x^5/(x^5-1) + 2x^6/[(x-1)*(x^2-1)*(x^3-1)] + 2x^6/[(x^2-1)*(x^4-1)] + x^6/(x^2-1)^3 + x^6/(x^3-1)^2 + x^7/[(x^3-1)*(x^4-1)] + x^7/[(x^2-1)*(x^5-1)] + x^7/[(x^2-1)^2*(x^3-1)] + x^8/[(x^3-1)*(x^5-1)]
CROSSREFS
Cf. A173548 (all magilatin squares), A173730 (symmetry types), A174018 (reduced squares by largest value), A174021 (reduced symmetry types by magic sum).
Sequence in context: A285223 A122412 A365413 * A356371 A293389 A128035
KEYWORD
nonn
AUTHOR
Thomas Zaslavsky, Mar 05 2010
EXTENSIONS
"Distinct" values (incorrect) deleted by Thomas Zaslavsky, Apr 24 2010
STATUS
approved

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