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A292155
Triangle T(m,k) read by rows, where T(m,k) is the number of ways in which 1<=k<=m positions can be picked in an m X m square grid such that the picked positions have a point symmetry but no line symmetry.
9
0, 0, 0, 0, 0, 0, 0, 0, 0, 112, 0, 0, 0, 528, 128, 0, 0, 0, 1800, 336, 5928, 0, 0, 0, 4908, 1156, 22628, 5676, 0, 0, 0, 11584, 2432, 71000, 14160, 333994
OFFSET
1,10
REFERENCES
Walter Krämer, Denkste! Trugschlüsse aus der Welt der Zahlen und des Zufalls. Campus Verlag, Frankfurt/Main, 1996.
FORMULA
a(n) = A292153(n) - A291718(n) = A291717(n) - A292154(n).
EXAMPLE
The triangle begins:
0;
0, 0;
0, 0, 0;
0, 0, 0, 112;
0, 0, 0, 528, 128;
0, 0, 0, 1800, 336, 5928;
0, 0, 0, 4908, 1156, 22628, 5676;
0, 0, 0, 11584, 2432, 71000, 14160, 333994;
.
The following configuration of 6 picked points from a 7X7 grid with a point symmetry but no line (mirror) symmetry is one of the T(7,6)=a(28)=22628 configurations with this property. It is of some historical interest, because when it was drawn in Germany's "Lotto 6 aus 49" in January 1988, there were 222 persons instead of typically 5-10 with a winning bet. They only won 31000 DM (Deutsche Mark) instead of the 1 million DM they had hoped for.
.
o o o o o o o
o o o o o o o
o o o o o o o
o o X X X o o
o X X X o o o
o o o o o o o
o o o o o o o
.
The shown configuration is also in A098485(28) (graph consisting of a single component).
KEYWORD
nonn,tabl,more
AUTHOR
Hugo Pfoertner, Sep 17 2017
STATUS
approved