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A174020 Number of reduced 3x3 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

T. Zaslavsky, Table of n, a(n) for n=3..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.: 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: A040133 A092538 A022346 * A173549 A299853 A251643

Adjacent sequences:  A174017 A174018 A174019 * A174021 A174022 A174023

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 21 19:57 EDT 2019. Contains 325199 sequences. (Running on oeis4.)