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%I #10 Jun 29 2023 09:41:14
%S 1,1,2,3,6,8,16,15,25,30,41,43,66,68,92,99,129,136,180,180,231,245,
%T 297,304,385,388,469,482,575,588,706,704,831,858,987,996,1171,1175,
%U 1350,1370,1561,1581,1806,1804,2047,2081,2323,2335,2641,2649,2951,2979,3302
%N Number of symmetry classes 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. The symmetries are row and column permutations and diagonal flip.
%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 Thomas Zaslavsky, <a href="/A174021/b174021.txt">Table of n, a(n) for n=3..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_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).
%Y Cf. A173549 (all magilatin squares), A173730 (symmetry types), A174020 (reduced squares), A174019 (reduced symmetry types by largest value).
%K nonn
%O 3,3
%A _Thomas Zaslavsky_, Mar 05 2010
%E "Distinct" values (incorrect) deleted by _Thomas Zaslavsky_, Apr 24 2010
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