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 A108577 Number of symmetry classes of 3 X 3 magic squares (with distinct positive entries) having all entries < n. 8

%I #8 Mar 19 2015 09:40:24

%S 0,0,0,0,0,0,0,0,0,1,2,5,8,12,16,23,30,40,50,63,76,93,110,132,154,180,

%T 206,238,270,308,346,390,434,485,536,595,654,720,786,861,936,1020,

%U 1104,1197,1290,1393,1496,1610,1724,1848,1972,2108,2244,2392,2540,2700,2860

%N Number of symmetry classes of 3 X 3 magic squares (with distinct positive entries) having all entries < n.

%C From _Thomas Zaslavsky_, Mar 12 2010: (Start)

%C 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. The symmetries are those of the square.

%C a(n) is given by a quasipolynomial of period 18. (End)

%H T. Zaslavsky, <a href="/A108577/b108577.txt">Table of n, a(n) for n = 1..10000</a>.

%H M. Beck and T. Zaslavsky, <a href="http://www.math.binghamton.edu/zaslav/Tpapers/index.html#SLS">Six little squares and how their numbers grow</a>, submitted. - _Thomas Zaslavsky_, Jan 29 2010

%H Matthias Beck and Thomas Zaslavsky, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Zaslavsky/sls.html">Six Little Squares and How their Numbers Grow</a>, Journal of Integer Sequences, 13 (2010), Article 10.6.2.

%F G.f.: (x^10*(2*x^2+1)) / ((1-x^6)*(1-x^4)*(1-x)^2) a(n) is given by a quasipolynomial of period 12.

%e a(10) = 1 because there is only one symmetry type of 3 X 3 magic square with entries 1,...,9.

%Y Cf. A108576, A108578, A108579.

%K nonn

%O 1,11

%A _Thomas Zaslavsky_, Jun 11 2005

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