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A174019 Number of symmetry classes of reduced 3x3 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

T. Zaslavsky, Table of n, a(n) for n=2..10000.

M. Beck, T. 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.

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: A293688 A285223 A122412 * A293389 A128035 A003473

Adjacent sequences:  A174016 A174017 A174018 * A174020 A174021 A174022

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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Last modified July 22 20:49 EDT 2019. Contains 325226 sequences. (Running on oeis4.)