A292156 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 line symmetry but no point symmetry.

0, 0, 0, 0, 0, 36, 0, 0, 168, 220, 0, 0, 524, 944, 1960, 0, 0, 1292, 2848, 6752, 15752, 0, 0, 2736, 7248, 20280, 55904, 120212, 0, 0, 5088, 15576, 48576, 156224, 378824, 1068008

Offset: 1

Author

Hugo Pfoertner, Sep 17 2017

Keywords

• nonn
• tabl
• more

Examples

			The triangle begins:
   0;
   0, 0;
   0, 0,   36;
   0, 0,  168,  220;
   0, 0,  524,  944,  1960;
   0, 0, 1292, 2848,  6752, 15752;
   0, 0, 2736, 7248, 20280, 55904, 120212;
.
The following configuration of 6 picked points from a 7X7 grid with a line (mirror) symmetry w.r.t. the line indicated by +++, but no point symmetry, is one of the T(7,6)=a(27)=55904 configurations with this property:
  o o o o o o o
  + X o X o o o
  X + o o o X o
  o o + o o o o
  X o o + o o o
  o o o o + o o
  o X o o o + o
		

Crossrefs

Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292153, A292154, A292155.

Formula

a(n) = A292153(n) - A291717(n) = A291718(n) - A292154(n).