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

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. - Thomas Zaslavsky, Mar 12 2010

Links

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

Matthias Beck and Thomas Zaslavsky, Auxiliary files for "Six little squares".

Matthias Beck and Thomas Zaslavsky, Six Little Squares and How their Numbers Grow, Journal of Integer Sequences, 13 (2010), Article 10.6.2.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,2,-2,1,0,-1,2,-1).

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.

Mathematica

LinearRecurrence[{2, -1, 0, 1, -2, 2, -2, 1, 0, -1, 2, -1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5}, 58] (* Mike Sheppard, Feb 04 2025 *)

Crossrefs

Cf. A108576, A108578, A108579.

Sequence in context: A229154 A362601 A174605 * A272719 A297834 A376356

Adjacent sequences: A108574 A108575 A108576 * A108578 A108579 A108580

Keyword

nonn,easy,changed

Author

Thomas Zaslavsky, Jun 11 2005

Status

approved