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 A173549 Number of 3 X 3 magilatin squares with positive values and magic sum n. 7

%I

%S 12,12,24,72,156,240,552,600,1020,1548,2004,2568,4008,4644,6264,8136,

%T 10152,12168,16284,18372,22992,27972,32736,37896,47352,52332,62004,

%U 72288,82572,93108,110280,120492,138420,157428,175248,193824,223428

%N Number of 3 X 3 magilatin squares with positive values and magic sum n.

%C A magilatin square has equal row and column sums and no number repeated in any row or column.

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

%H Matthias Beck and Thomas Zaslavsky, <a href="https://arxiv.org/abs/math/0506315">An enumerative geometry for magic and magilatin labellings</a>, arXiv:math/0506315 [math.CO], 2005

%H Matthias Beck and Thomas Zaslavsky, <a href="https://doi.org/10.1007/s00026-006-0296-4">An enumerative geometry for magic and magilatin labellings</a>, Annals of Combinatorics, 10 (2006), no. 4, pages 395-413. MR 2007m:05010. Zbl 1116.05071.

%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>, Journal of Integer Sequences, 13 (2010), Article 10.6.2.

%F G.f.: x^3/(1-x^3) * { 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)] }.

%t LinearRecurrence[{-2, -3, -2, 0, 3, 6, 8, 9, 7, 3, -4, -10, -15, -16, -14, -8, 0, 8, 14, 16, 15, 10, 4, -3, -7, -9, -8, -6, -3, 0, 2, 3, 2, 1}, {0, 0, 0, 0, 0, 12, 12, 24, 72, 156, 240, 552, 600, 1020, 1548, 2004, 2568, 4008, 4644, 6264, 8136, 10152, 12168, 16284, 18372, 22992, 27972, 32736, 37896, 47352, 52332, 62004, 72288, 82572}, 42][[6;;]] (* _Jean-François Alcover_, Nov 06 2018 *)

%Y Cf. A173730 (symmetry types), A173548 (counted by upper bound), A173729 (symmetry types by upper bound).

%K nonn

%O 6,1

%A _Thomas Zaslavsky_, Mar 04 2010, Apr 24 2010

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Last modified August 22 17:23 EDT 2019. Contains 326180 sequences. (Running on oeis4.)