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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A174020 #16 Jun 29 2023 09:39:53
%S A174020 12,12,24,60,144,216,480,444,780,996,1404,1548,2460,2640,3696,4128,
%T A174020 5508,5904,8148,8220,10824,11688,14364,14904,19380,19596,24108,24936,
%U A174020 30240,31104,37992,37920,45312,47148,54756,55404,66000,66252,76920,78288
%N A174020 Number of reduced 3 X 3 magilatin squares with magic sum n.
%C A174020 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 A174020 a(n) is given by a quasipolynomial of degree 4 and period 840.
%D A174020 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 A174020 Thomas Zaslavsky, <a href="/A174020/b174020.txt">Table of n, a(n) for n = 3..10000</a>.
%H A174020 Matthias Beck and Thomas 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 A174020 Matthias Beck and Thomas Zaslavsky, <a href="https://people.math.binghamton.edu/zaslav/Tpapers/SLSfiles/">"Six Little Squares and How their Numbers Grow" Web Site</a>: Maple worksheets and supporting documentation.
%H A174020 <a href="/index/Rec#order_31">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A174020 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 A174020 Cf. A173549 (all magilatin squares), A173730 (symmetry types), A174021 (reduced symmetry types), A174018 (reduced squares by largest value).
%K A174020 nonn
%O A174020 3,1
%A A174020 _Thomas Zaslavsky_, Mar 05 2010
%E A174020 "Distinct" values (incorrect) deleted by _Thomas Zaslavsky_, Apr 24 2010