

A174018


Number of reduced 3x3 magilatin squares with largest entry n.


3



12, 24, 36, 192, 420, 720, 1020, 1752, 2268, 3648, 4596, 6624, 8148, 11112, 12924, 17328, 20076, 25488, 28452, 36312, 39924, 49152, 54060, 64944, 70716, 84696, 90612, 106896, 114756, 133200, 141708, 164184, 173340, 198192, 209796, 237600
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OFFSET

2,1


COMMENTS

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.
a(n) is given by a quasipolynomial of degree 5 and period 60.


REFERENCES

Matthias Beck and Thomas Zaslavsky, An enumerative geometry for magic and magilatin labellings, Annals of Combinatorics, 10 (2006), no. 4, pages 395413. MR 2007m:05010. Zbl 1116.05071.


LINKS

T. Zaslavsky, Table of n, a(n) for n=2..10000.
M. Beck, T. Zaslavsky, Six Little Squares and How Their Numbers Grow , J. Int. Seq. 13 (2010), 10.6.2.
Matthias Beck and Thomas Zaslavsky, "Six Little Squares and How their Numbers Grow" Web Site: Maple worksheets and supporting documentation.


FORMULA

G.f.: 12x^2/(x1)^2  36x^3/(x1)^3  72x^3/[(x1)*(x^21)]  36x^3/(x^31)  72x^4/[(x1)^2*(x^21)]  36x^4/[(x1)*(x^31)]  72x^4/(x^21)^2 + 72x^5/[(x1)^3*(x^21)] + 72x^5/[(x1)^2*(x^31)] + 144x^5/[(x1)*(x^21)^2] + 72x^5/[(x1)*(x^41)] + 108x^5/[(x^21)*(x^31)] + 72x^5/(x^51) + 144x^6/[(x1)*(x^21)*(x^31)] + 72x^6/(x^21)^3 + 144x^6/[(x^21)*(x^41)] + 72x^6/(x^31)^2 + 72x^7/[(x^21)^2*(x^31)] + 72x^7/[(x^21)*(x^51)] + 72x^7/[(x^31)*(x^41)] + 72x^8/[(x^31)*(x^51)]


CROSSREFS

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).
Sequence in context: A117304 A022759 A091193 * A098242 A139406 A140831
Adjacent sequences: A174015 A174016 A174017 * A174019 A174020 A174021


KEYWORD

nonn


AUTHOR

Thomas Zaslavsky, Mar 05 2010


EXTENSIONS

"Distinct" values (incorrect) deleted by Thomas Zaslavsky, Apr 24 2010


STATUS

approved



