%I
%S 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,
%T 1156,22628,5676,0,0,0,11584,2432,71000,14160,333994
%N 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.
%D Walter Krämer, Denkste! Trugschlüsse aus der Welt der Zahlen und des Zufalls. Campus Verlag, Frankfurt/Main, 1996.
%F a(n) = A292153(n)  A291718(n) = A291717(n)  A292154(n).
%e The triangle begins:
%e 0;
%e 0, 0;
%e 0, 0, 0;
%e 0, 0, 0, 112;
%e 0, 0, 0, 528, 128;
%e 0, 0, 0, 1800, 336, 5928;
%e 0, 0, 0, 4908, 1156, 22628, 5676;
%e 0, 0, 0, 11584, 2432, 71000, 14160, 333994;
%e .
%e 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 510 with a winning bet. They only won 31000 DM (Deutsche Mark) instead of the 1 million DM they had hoped for.
%e .
%e o o o o o o o
%e o o o o o o o
%e o o o o o o o
%e o o X X X o o
%e o X X X o o o
%e o o o o o o o
%e o o o o o o o
%e .
%e The shown configuration is also in A098485(28) (graph consisting of a single component).
%Y Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292153, A292154, A292156.
%K nonn,tabl,more
%O 1,10
%A _Hugo Pfoertner_, Sep 17 2017
