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A108579
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Number of symmetry classes of 3 X 3 magic squares (with distinct positive entries) having magic sum 3n.
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7
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0, 0, 0, 0, 1, 3, 4, 7, 10, 13, 17, 22, 26, 32, 38, 44, 51, 59, 66, 75, 84, 93, 103, 114, 124, 136, 148, 160, 173, 187, 200, 215, 230, 245, 261, 278, 294, 312, 330, 348, 367, 387, 406, 427, 448, 469, 491, 514, 536, 560, 584, 608, 633, 659, 684, 711, 738, 765, 793, 822, 850
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| A magic square has distinct positive integers in its cells, whose sum is the same (the "magic sum") along any row, column, or main diagonal.
a(n) is given by a quasipolynomial of period 6.
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REFERENCES
| M. Beck and T. Zaslavsky, Six little squares and how their numbers grow, in preparation.
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LINKS
| T. Zaslavsky, Table of n, a(n) for n=1,..,10000.
M. Beck and T. Zaslavsky, Six little squares and how their numbers grow, submitted. [From Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Jan 29 2010]
Matthias Beck and Thomas Zaslavsky, "Six Little Squares and How their Numbers Grow" Web Site: Maple worksheets and supporting documentation. [From Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Mar 12 2010]
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FORMULA
| G.f.: x^5*(1+2*x)/((1-x)*(1-x^2)*(1-x^3)).
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EXAMPLE
| a(5) = 1 because there is a unique 3 X 3 magic square, up to symmetry, using the first 9 positive integers.
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CROSSREFS
| Cf. A108576, A108577, A108578.
Nonzero entries are the second differences of A055328.
Sequence in context: A137294 A177959 A108855 * A050572 A105343 A147789
Adjacent sequences: A108576 A108577 A108578 * A108580 A108581 A108582
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KEYWORD
| nonn
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AUTHOR
| Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Jun 11 2005
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EXTENSIONS
| Edited by N. J. A. Sloane, Oct 04 2010
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