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%I #16 Jun 29 2023 09:38:01
%S 12,24,36,192,420,720,1020,1752,2268,3648,4596,6624,8148,11112,12924,
%T 17328,20076,25488,28452,36312,39924,49152,54060,64944,70716,84696,
%U 90612,106896,114756,133200,141708,164184,173340,198192,209796,237600
%N Number of reduced 3 X 3 magilatin squares with largest entry 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 5 and period 60.
%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 Thomas Zaslavsky, <a href="/A174018/b174018.txt">Table of n, a(n) for n = 2..10000</a>.
%H 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 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 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (-2, -1, 2, 5, 5, 2, -3, -7, -7, -3, 2, 5, 5, 2, -1, -2, -1).
%F 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)].
%Y 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).
%K nonn
%O 2,1
%A _Thomas Zaslavsky_, Mar 05 2010
%E "Distinct" values (incorrect) deleted by _Thomas Zaslavsky_, Apr 24 2010
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