

A174019


Number of symmetry classes of reduced 3 X 3 magilatin squares with largest entry n.


3



1, 2, 3, 8, 15, 24, 32, 52, 63, 94, 114, 156, 184, 244, 276, 358, 406, 504, 555, 692, 752, 910, 991, 1174, 1267, 1498, 1593, 1858, 1983, 2280, 2414, 2772, 2915, 3308, 3488, 3924, 4114, 4622, 4816, 5374, 5616, 6216, 6467, 7154, 7418, 8158, 8469, 9264, 9587
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OFFSET

2,2


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. The symmetries are row and column permutations and diagonal flip.
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

Index entries for linear recurrences with constant coefficients, signature (2, 1, 2, 5, 5, 2, 3, 7, 7, 3, 2, 5, 5, 2, 1, 2, 1).


FORMULA

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


CROSSREFS

Cf. A173548 (all magilatin squares), A173730 (symmetry types), A174018 (reduced squares by largest value), A174021 (reduced symmetry types by magic sum).


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



