|
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 1,11
|
|
|
COMMENTS
| Contribution from Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), 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)
|
|
|
REFERENCES
| M. Beck and T. Zaslavsky, Six little squares and how their numbers grow, in preparation.
|
|
|
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. [From Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Jan 29 2010]
Matthias Beck and Thomas Zaslavsky, "Six Little Squares and How their Numbers Grow" Web Site: Maple worksheets and supporting documentation. [From Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Mar 12 2010]
|
|
|
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: A134925 A184430 A174605 * A036789 A002960 A022942
Adjacent sequences: A108574 A108575 A108576 * A108578 A108579 A108580
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Thomas Zaslavsky (zaslav(AT)math.binghamton.edu), Jun 11 2005
|
| |
|
|
