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A174020 Number of reduced 3 X 3 magilatin squares with magic sum n. 3
12, 12, 24, 60, 144, 216, 480, 444, 780, 996, 1404, 1548, 2460, 2640, 3696, 4128, 5508, 5904, 8148, 8220, 10824, 11688, 14364, 14904, 19380, 19596, 24108, 24936, 30240, 31104, 37992, 37920, 45312, 47148, 54756, 55404, 66000, 66252, 76920, 78288 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
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 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
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).
FORMULA
G.f.: 12*x^3/[(x-1)*(x^2-1)] - 108*x^5/[(x-1)*(x^2-1)^2] - 72*x^5/[(x-1)*(x^4-1)] - 72*x^5/[(x^3-1)*(x^2-1)] - 36*x^5/(x^5-1) + 72*x^7/[(x-1)*(x^2-1)^3] + 144*x^7/[(x-1)*(x^2-1)*(x^4-1)] + 72*x^7/[(x-1)*(x^6-1)] + 72*x^7/[(x^2-1)^2*(x^3-1)] + 72*x^7/[(x^2-1)*(x^5-1)] + 72*x^7/(x^7-1) + 72*x^9/[(x-1)*(x^4-1)^2] + 144*x^9/[(x^2-1)*(x^3-1)*(x^4-1)] + 144*x^9/[(x^3-1)*(x^6-1)] + 72*x^9/[(x^4-1)*(x^5-1)] + 72*x^11/[(x^3-1)*(x^4-1)^2] + 72*x^11/[(x^3-1)*(x^8-1)] + 72*x^11/[(x^5-1)*(x^6-1)] + 72*x^13/[(x^5-1)*(x^8-1)].
CROSSREFS
Cf. A173549 (all magilatin squares), A173730 (symmetry types), A174021 (reduced symmetry types), A174018 (reduced squares by largest value).
Sequence in context: A309772 A335778 A022346 * A173549 A299853 A251643
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 June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)