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A173549 Number of 3 X 3 magilatin squares with positive values and magic sum n. 8
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, 93108, 110280, 120492, 138420, 157428, 175248, 193824, 223428 (list; graph; refs; listen; history; text; internal format)
OFFSET
6,1
COMMENTS
A magilatin square has equal row and column sums and no number repeated in any row or column.
a(n) is given by a quasipolynomial of degree 4 and period 840.
LINKS
Matthias Beck and Thomas Zaslavsky, An enumerative geometry for magic and magilatin labellings, arXiv:math/0506315 [math.CO], 2005
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.
Matthias Beck and Thomas Zaslavsky, Six Little Squares and How their Numbers Grow, Journal of Integer Sequences, 13 (2010), Article 10.6.2.
Index entries for linear recurrences with constant coefficients, signature (-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).
FORMULA
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)] }.
MATHEMATICA
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 *)
CROSSREFS
Cf. A173730 (symmetry types), A173548 (counted by upper bound), A173729 (symmetry types by upper bound).
Sequence in context: A335778 A022346 A174020 * A299853 A251643 A346531
KEYWORD
nonn
AUTHOR
Thomas Zaslavsky, Mar 04 2010, Apr 24 2010
STATUS
approved

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