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%I #13 Sep 20 2017 05:08:38
%S 0,0,0,0,0,40,0,0,368,1432,0,0,1704,10992,50992,0,0,5704,53784,369776,
%T 1925464,0,0,15400,198696,1885128,13903624,85773968,0,0,36096,606264,
%U 7572896,74743584,620821688,4424756040
%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 don't have any symmetry.
%D Walter Krämer, Denkste! Trugschlüsse aus der Welt der Zahlen und des Zufalls. Campus Verlag, Frankfurt/Main, 1996. Chapter 4, pp. 71-82.
%F a(n) = A090642(n) - A292153(n).
%e The triangle begins:
%e 0;
%e 0, 0;
%e 0, 0, 40;
%e 0, 0, 368, 1432;
%e 0, 0, 1704, 10992, 50992;
%e 0, 0, 5704, 53784, 369776, 1925464;
%e 0, 0, 15400, 198696, 1885128, 13903624, 85773968;
%e .
%e The following configuration of 6 picked points from a 7X7 grid is one of the T(7,6)=a(28)=13903624 configurations without symmetry. It is of some historical interest, because when it was drawn in Germany's "Lotto 6 aus 49", there was only one person with a winning bet receiving a payout of 22 million DM (Deutsche Mark).
%e .
%e o o o o o o o
%e o o o o o o o
%e o o o o X o o
%e o o X o o o o
%e o o o o o o X
%e X X X o o o o
%e o o o o o o o
%Y Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292153, A292154, A292155, A292156.
%K nonn,tabl,more
%O 1,6
%A _Hugo Pfoertner_, Sep 17 2017
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