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A174021
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Number of symmetry classes of reduced 3x3 magilatin squares with magic sum n.
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4
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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
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OFFSET
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3,3
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COMMENTS
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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.
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REFERENCES
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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.
Matthias Beck and Thomas Zaslavsky, Six little squares and how their numbers grow, in preparation.
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LINKS
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T. Zaslavsky, Table of n, a(n) for n=3..10000.
Matthias Beck and Thomas Zaslavsky, "Six Little Squares and How their Numbers Grow" Web Site: Maple worksheets and supporting documentation.
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FORMULA
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G.f.:
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CROSSREFS
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Cf. A173549 (all magilatin squares), A173730 (symmetry types), A174020 (reduced squares), A174019 (reduced symmetry types by largest value).
Sequence in context: A209405 A048809 A047001 * A091070 A133586 A141348
Adjacent sequences: A174018 A174019 A174020 * A174022 A174023 A174024
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KEYWORD
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nonn
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AUTHOR
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Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Mar 05 2010
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EXTENSIONS
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"Distinct" values (incorrect) deleted by Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Apr 24 2010
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STATUS
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approved
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