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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.

%I A292155 #14 Sep 20 2017 05:09:11
%S A292155 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 A292155 1156,22628,5676,0,0,0,11584,2432,71000,14160,333994
%N 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.
%D A292155 Walter Krämer, Denkste! Trugschlüsse aus der Welt der Zahlen und des Zufalls. Campus Verlag, Frankfurt/Main, 1996.
%F A292155 a(n) = A292153(n) - A291718(n) = A291717(n) - A292154(n).
%e A292155 The triangle begins:
%e A292155    0;
%e A292155    0, 0;
%e A292155    0, 0, 0;
%e A292155    0, 0, 0,   112;
%e A292155    0, 0, 0,   528,  128;
%e A292155    0, 0, 0,  1800,  336,  5928;
%e A292155    0, 0, 0,  4908, 1156, 22628,  5676;
%e A292155    0, 0, 0, 11584, 2432, 71000, 14160, 333994;
%e A292155 .
%e A292155 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.
%e A292155 .
%e A292155   o o o o o o o
%e A292155   o o o o o o o
%e A292155   o o o o o o o
%e A292155   o o X X X o o
%e A292155   o X X X o o o
%e A292155   o o o o o o o
%e A292155   o o o o o o o
%e A292155 .
%e A292155 The shown configuration is also in A098485(28) (graph consisting of a single component).
%Y A292155 Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292153, A292154, A292156.
%K A292155 nonn,tabl,more
%O A292155 1,10
%A A292155 _Hugo Pfoertner_, Sep 17 2017