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

1,2

Comments

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

Links

Table of n, a(n) for n=1..36.

Formula

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

Example

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.

Sequence in context: A292154 A291717 A303699 * A175459 A257652 A107665

Adjacent sequences: A292150 A292151 A292152 * A292154 A292155 A292156

Keyword

nonn,tabl

Author

Hugo Pfoertner, Sep 17 2017

Status

approved