A292152 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.

0, 0, 0, 0, 0, 40, 0, 0, 368, 1432, 0, 0, 1704, 10992, 50992, 0, 0, 5704, 53784, 369776, 1925464, 0, 0, 15400, 198696, 1885128, 13903624, 85773968, 0, 0, 36096, 606264, 7572896, 74743584, 620821688, 4424756040

Offset: 1

Author

Hugo Pfoertner, Sep 17 2017

Keywords

• nonn
• tabl
• more

Examples

			The triangle begins:
  0;
  0,  0;
  0,  0,    40;
  0,  0,   368,   1432;
  0,  0,  1704,  10992,  50992;
  0,  0,  5704,  53784,  369776,  1925464;
  0,  0, 15400, 198696, 1885128, 13903624, 85773968;
.
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).
.
  o o o o o o o
  o o o o o o o
  o o o o X o o
  o o X o o o o
  o o o o o o X
  X X X o o o o
  o o o o o o o
		

References

• Walter Krämer, Denkste! Trugschlüsse aus der Welt der Zahlen und des Zufalls. Campus Verlag, Frankfurt/Main, 1996. Chapter 4, pp. 71-82.

Crossrefs

Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292153, A292154, A292155, A292156.

Formula

a(n) = A090642(n) - A292153(n).