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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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A229154 A362601 A174605 * A272719 A297834 A036789
KEYWORD
nonn
AUTHOR
Thomas Zaslavsky, Jun 11 2005
STATUS
approved

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Last modified June 19 15:28 EDT 2024. Contains 373503 sequences. (Running on oeis4.)