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.

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

Author

Hugo Pfoertner, Sep 17 2017

Keywords

• nonn
• tabl
• more

Examples

			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).
		

References

• Walter Krämer, Denkste! Trugschlüsse aus der Welt der Zahlen und des Zufalls. Campus Verlag, Frankfurt/Main, 1996.

Crossrefs

Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292153, A292154, A292156.

Formula

a(n) = A292153(n) - A291718(n) = A291717(n) - A292154(n).