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A173546 Number of 3x3 semimagic squares with distinct positive values < n. In a semimagic squares the row and column sums must all be equal (the "magic sum"). 5
72, 288, 936, 2592, 5760, 11520, 20952, 35712, 57168, 88272, 131112, 189504, 265752, 365760, 492480, 653040, 851472, 1096416, 1392768, 1751904, 2178864, 2687184, 3283632, 3983760, 4794984, 5736528, 6816456, 8056224, 9466128 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,1

COMMENTS

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 395-413. MR 2007m:05010. Zbl 1116.05071.

LINKS

T. Zaslavsky, Table of n, a(n) for n=10..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.: 72 * x^2/(1-x)^2 * { x^5/[(1-x)^3*(1-x^2)] - 2x^5/[(1-x)*(1-x^2)^2] - x^5/[(1-x)^2*(1-x^3)] - 2x^6/[(1-x)*(1-x^2)*(1-x^3)] - x^6/(1-x^2)^3 - x^7/[(1-x^2)^2*(1-x^3)] + x^5/[(1-x)*(1-x^4)] + 2x^5/[(1-x^2)*(1-x^3)] + 2x^6/[(1-x^2)*(1-x^4)] + x^6/(1-x^3)^2 + x^7/[(1-x^2)*(1-x^5)] + x^7/[(1-x^3)*(1-x^4)] + x^8/[(1-x^3)*(1-x^5)] - x^5/(1-x^5) } [From Thomas Zaslavsky, Mar 03 2010]

CROSSREFS

A173547 counts the same squares by magic sum. Cf. A108576, A108577, A108578, A108579, A173548, A173549.

Sequence in context: A316800 A004007 A279272 * A308136 A242534 A277430

Adjacent sequences:  A173543 A173544 A173545 * A173547 A173548 A173549

KEYWORD

nonn

AUTHOR

Thomas Zaslavsky, Feb 21 2010

STATUS

approved

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Last modified August 19 20:20 EDT 2019. Contains 326133 sequences. (Running on oeis4.)