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A174018
Number of reduced 3 X 3 magilatin squares with largest entry n.
3
12, 24, 36, 192, 420, 720, 1020, 1752, 2268, 3648, 4596, 6624, 8148, 11112, 12924, 17328, 20076, 25488, 28452, 36312, 39924, 49152, 54060, 64944, 70716, 84696, 90612, 106896, 114756, 133200, 141708, 164184, 173340, 198192, 209796, 237600
OFFSET
2,1
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.
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.: 12x^2/(x-1)^2 - 36x^3/(x-1)^3 - 72x^3/[(x-1)*(x^2-1)] - 36x^3/(x^3-1) - 72x^4/[(x-1)^2*(x^2-1)] - 36x^4/[(x-1)*(x^3-1)] - 72x^4/(x^2-1)^2 + 72x^5/[(x-1)^3*(x^2-1)] + 72x^5/[(x-1)^2*(x^3-1)] + 144x^5/[(x-1)*(x^2-1)^2] + 72x^5/[(x-1)*(x^4-1)] + 108x^5/[(x^2-1)*(x^3-1)] + 72x^5/(x^5-1) + 144x^6/[(x-1)*(x^2-1)*(x^3-1)] + 72x^6/(x^2-1)^3 + 144x^6/[(x^2-1)*(x^4-1)] + 72x^6/(x^3-1)^2 + 72x^7/[(x^2-1)^2*(x^3-1)] + 72x^7/[(x^2-1)*(x^5-1)] + 72x^7/[(x^3-1)*(x^4-1)] + 72x^8/[(x^3-1)*(x^5-1)].
CROSSREFS
Cf. A173548 (all magilatin squares), A173730 (symmetry types), A174019 (reduced symmetry types by largest value), A174020 (reduced squares by magic sum), A174021 (reduced symmetry types by magic sum).
Sequence in context: A335540 A091193 A335541 * A098242 A139406 A140831
KEYWORD
nonn
AUTHOR
Thomas Zaslavsky, Mar 05 2010
EXTENSIONS
"Distinct" values (incorrect) deleted by Thomas Zaslavsky, Apr 24 2010
STATUS
approved