A292153 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 or a line symmetry.

1, 4, 6, 9, 36, 44, 16, 120, 192, 388, 25, 300, 596, 1658, 2138, 36, 630, 1436, 5121, 7216, 22328, 49, 1176, 3024, 13180, 21756, 80192, 126616, 64, 2016, 5568, 29112, 51616, 230784, 394504, 1409328

Offset: 1

Author

Hugo Pfoertner, Sep 17 2017

Keywords

• nonn
• tabl

Comments

The "or" is inclusive, i.e. configurations that have both types of symmetry simultaneously (counted separately in A292154) are included.

Examples

			The triangle begins:
   1;
   4,    6;
   9,   36,   44;
  16,  120,  192,   388;
  25,  300,  596,  1658,  2138;
  36,  630, 1436,  5121,  7216, 22328;
  49, 1176, 3024, 13180, 21756, 80192, 126616;
.
The following configuration is one of the T(4,3)=a(9)=192 symmetric configurations of 3 points picked from a 4 X 4 grid. It has both types of symmetry.
  0 0 0 0
  X 0 0 0
  0 X 0 0
  0 0 X 0
		

Crossrefs

Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292154, A292155, A292156.

Formula

a(n) = A090642(n) - A292152(n) = A292154(n) + A292155(n) + A292156(n).