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

Table of n, a(n) for n=6..42.

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.

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-Fran├žois Alcover, Nov 06 2018 *)

CROSSREFS

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

Sequence in context: A092538 A022346 A174020 * A299853 A251643 A070710

Adjacent sequences:  A173546 A173547 A173548 * A173550 A173551 A173552

KEYWORD

nonn

AUTHOR

Thomas Zaslavsky, Mar 04 2010, Apr 24 2010

STATUS

approved

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Last modified July 18 11:48 EDT 2019. Contains 325139 sequences. (Running on oeis4.)