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

1,10

References

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

Links

Table of n, a(n) for n=1..36.

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).

Crossrefs

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

Sequence in context: A261820 A262661 A156407 * A341011 A103849 A340470

Adjacent sequences: A292152 A292153 A292154 * A292156 A292157 A292158

Keyword

nonn,tabl,more

Author

Hugo Pfoertner, Sep 17 2017

Status

approved