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A173547 Number of 3 X 3 semimagic squares with distinct positive values and magic sum n. 5
72, 144, 288, 576, 864, 1440, 2088, 3024, 3888, 5904, 6984, 9432, 12168, 14904, 17928, 23832, 26784, 33048, 39672, 46584, 53640, 65592, 72504, 85248, 98928, 111816, 125208, 147528, 160632, 182808, 206424, 229176, 252648, 287928, 310752 (list; graph; refs; listen; history; text; internal format)
OFFSET

15,1

COMMENTS

In a semimagic squares the row and column sums must all be equal to the magic sum. a(n) is given by a quasipolynomial of degree 4 and period 840.

a(15) is the first term because the values 1,...,9 make magic sum 15. [From Thomas Zaslavsky, Mar 03 2010]

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=15..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^3/(1-x)^3 * { x^7/[(x-1)*(x^2-1)^3] + 2x^7/[(x-1)*(x^2-1)*(x^4-1)] + x^7/[(x-1)*(x^6-1)] + x^7/[(x^2-1)^2*(x^3-1)] + x^7/[(x^2-1)*(x^5-1)] + x^7/[(x^3-1)*(x^4-1)] + x^7/(x^7-1) + x^9/[(x-1)*(x^4-1)^2] + 2*x^9/[(x^2-1)*(x^3-1)*(x^4-1)] + 2*x^9/[(x^3-1)*(x^6-1)] + x^9/[(x^4-1)*(x^5-1)] + x^11/[(x^3-1)*(x^4-1)^2] + x^11/[(x^3-1)*(x^8-1)] + x^11/[(x^5-1)*(x^6-1)] + x^13/[(x^5-1)*(x^8-1)] }

CROSSREFS

A173546 counts the same squares by upper bound on the entries. Cf. A108576, A108577, A108578, A108579, A173548, A173549.

Sequence in context: A050495 A137883 A173728 * A173727 A039498 A063357

Adjacent sequences:  A173544 A173545 A173546 * A173548 A173549 A173550

KEYWORD

nonn

AUTHOR

Thomas Zaslavsky, Feb 21 2010, Feb 24 2010, Mar 03 2010

STATUS

approved

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Last modified August 22 05:00 EDT 2019. Contains 326172 sequences. (Running on oeis4.)