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

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

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)) / ((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

Cf. A108576, A108578, A108579.

Sequence in context: A229154 A362601 A174605 * A272719 A297834 A036789

Adjacent sequences: A108574 A108575 A108576 * A108578 A108579 A108580

Keyword

nonn

Author

Thomas Zaslavsky, Jun 11 2005

Status

approved