

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

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



FORMULA

G.f.: (x^10*(2*x^2+1)) / ((1x^6)*(1x^4)*(1x)^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



STATUS

approved



