A291718 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.

1, 4, 6, 8, 36, 44, 16, 120, 192, 276, 25, 300, 596, 1130, 2010, 36, 630, 1436, 3321, 6880, 16400, 49, 1176, 3024, 8272, 20600, 57564, 120940, 64, 2016, 5568, 17528, 49184, 159784, 380344, 1075344

Offset: 1

Author

Hugo Pfoertner, Sep 08 2017

Keywords

• nonn
• tabl
• more

Examples

			A configuration of 6 picked points from a 7 X 7 grid with a line (mirror) symmetry w.r.t. the line indicated by +++, and no point symmetry would be:
  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
So it would not contribute to the count of central symmetric configurations in A291717(27).
.
A configuration
  o o + o o o o
  o o + o o o o
  X o + o X o o
  + X # X + + +
  X o + o X o o
  o o + o o o o
  o o + o o o o
would contribute both to a(27) and to A291717(27), because besides being mirror symmetric w.r.t. the lines indicated by +++, it has also a central symmetry w.r.t the point indicated by #.
.
Triangle begins:
   1;
   4,    6;
   9,   36,   44;
  16,  120,  192,   276;
  25,  300,  596,  1130,  2010;
  36,  630, 1436,  3321,  6880,  16400;
  49, 1176, 3024,  8272, 20600,  57564, 120940;
  64, 2016, 5568, 17528, 49184, 159784, 380344, 1075344;
		

Crossrefs

Cf. A090642, A098485, A098487, A291716, A291717, A292152, A292153, A292154, A292155, A292156.