

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
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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

T. Zaslavsky, Table of n, a(n) for n = 1..10000.
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)) / ((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

Cf. A108576, A108578, A108579.
Sequence in context: A213707 A229154 A174605 * A272719 A297834 A036789
Adjacent sequences: A108574 A108575 A108576 * A108578 A108579 A108580


KEYWORD

nonn


AUTHOR

Thomas Zaslavsky, Jun 11 2005


STATUS

approved



