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A108577
Number of symmetry classes of 3 X 3 magic squares (with distinct positive entries) having all entries < n.
8
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, 206, 238, 270, 308, 346, 390, 434, 485, 536, 595, 654, 720, 786, 861, 936, 1020, 1104, 1197, 1290, 1393, 1496, 1610, 1724, 1848, 1972, 2108, 2244, 2392, 2540, 2700, 2860
OFFSET
1,11
COMMENTS
From Thomas Zaslavsky, 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. The symmetries are those of the square.
a(n) is given by a quasipolynomial of period 18. (End)
LINKS
M. Beck and T. Zaslavsky, Six little squares and how their numbers grow, submitted. - Thomas Zaslavsky, Jan 29 2010
Matthias Beck and Thomas Zaslavsky, Six Little Squares and How their Numbers Grow, Journal of Integer Sequences, 13 (2010), Article 10.6.2.
FORMULA
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.
EXAMPLE
a(10) = 1 because there is only one symmetry type of 3 X 3 magic square with entries 1,...,9.
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Zaslavsky, Jun 11 2005
STATUS
approved