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A174020 Number of reduced 3x3 magilatin squares with magic sum n. 3


%S 12,12,24,60,144,216,480,444,780,996,1404,1548,2460,2640,3696,4128,

%T 5508,5904,8148,8220,10824,11688,14364,14904,19380,19596,24108,24936,

%U 30240,31104,37992,37920,45312,47148,54756,55404,66000,66252,76920,78288

%N Number of reduced 3x3 magilatin squares with magic sum n.

%C 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.

%C a(n) is given by a quasipolynomial of degree 4 and period 840.

%D 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.

%H T. Zaslavsky, <a href="/A174020/b174020.txt">Table of n, a(n) for n=3..10000</a>.

%H M. Beck, T. Zaslavsky, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Zaslavsky/sls.html">Six Little Squares and How Their Numbers Grow </a>, J. Int. Seq. 13 (2010), 10.6.2.

%H Matthias Beck and Thomas Zaslavsky, <a href="http://www.math.binghamton.edu/zaslav/Tmath/SLSfiles/">"Six Little Squares and How their Numbers Grow" Web Site</a>: Maple worksheets and supporting documentation.

%F 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)]

%Y Cf. A173549 (all magilatin squares), A173730 (symmetry types), A174021 (reduced symmetry types), A174018 (reduced squares by largest value).

%K nonn

%O 3,1

%A _Thomas Zaslavsky_, Mar 05 2010

%E "Distinct" values (incorrect) deleted by _Thomas Zaslavsky_, Apr 24 2010

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Last modified August 23 01:10 EDT 2019. Contains 326211 sequences. (Running on oeis4.)