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A108578
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Number of 3 X 3 magic squares with magic sum 3n.
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7
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0, 0, 0, 0, 8, 24, 32, 56, 80, 104, 136, 176, 208, 256, 304, 352, 408, 472, 528, 600, 672, 744, 824, 912, 992, 1088, 1184, 1280, 1384, 1496, 1600, 1720, 1840, 1960, 2088, 2224, 2352, 2496, 2640, 2784, 2936, 3096, 3248, 3416, 3584, 3752, 3928, 4112, 4288
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Contribution from Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Mar 12 2010: (Start)
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. (End)
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LINKS
| T. Zaslavsky, Table of n, a(n) for n=1,..,10000.
M. Beck and T. Zaslavsky, An enumerative geometry for magic and magilatin labellings, Ann. Combinatorics, 10 (2006), no. 4, 395-413. MR 2007m:05010. Zbl 1116.05071. [From Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Jan 29 2010]
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.: [8*x^5*(1+2*x)] / [(1-x)*(1-x^2)*(1-x^3)]
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EXAMPLE
| a(5) = 8 because there are 8 3 X 3 magic squares with entries 1,...,9 and magic sum 15.
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PROG
| (PARI) a(n)=(1/9)*(2*n^2-32*n+[144, 78, 120, 126, 96, 102][(n%18)/3+1])
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CROSSREFS
| Equals 8 times the second differences of A055328.
Cf. A108576, A108577, A108579.
Sequence in context: A028628 A128690 A140403 * A044450 A134223 A050427
Adjacent sequences: A108575 A108576 A108577 * A108579 A108580 A108581
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KEYWORD
| nonn
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AUTHOR
| Thomas Zaslavsky (zaslav(AT)math.binghamton.edu) and Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 11 2005
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EXTENSIONS
| Edited by N, J. A. Sloane, Feb 05 2010
Corrected g.f. to account for previous change in parameter n from magic sum s to s/3; by Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Mar 12 2010
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