A292154 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 both a point symmetry and a line symmetry.

1, 4, 6, 9, 36, 8, 16, 120, 24, 56, 25, 300, 72, 186, 50, 36, 630, 144, 473, 128, 648, 49, 1176, 288, 1024, 320, 1660, 728, 64, 2016, 480, 1952, 608, 3560, 1520, 7326

Offset: 1

Author

Hugo Pfoertner, Sep 17 2017

Keywords

• nonn
• tabl
• more

Examples

			The triangle begins:
   1;
   4,    6;
   9,   36,   8;
  16,  120,  24,   56;
  25,  300,  72,  186,  50;
  36,  630, 144,  473, 128,  648;
  49, 1176, 288, 1024, 320, 1660,  728;
  64, 2016, 480, 1952, 608, 3560, 1520, 7326;
.
  o o o o o o
  X o o X o o
  o o o o o o
  X o o X o o
  o o o o o o
  X o o X o o
is one of the T(6,6)=a(21)=648 configurations with both types of symmetry.
.
  o o X o o o
  o X o o o o
  o o o X o o
  o o o o o X
  o o o o X o
  o o o o o o
is one of the T(6,5)=a(20)=128 configurations with both types of symmetry.
		

Crossrefs

Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292153, A292155, A292156.

Formula

a(n) = A292153(n) - A292155(n) - A292156(n).

a(n) = A291717(n) - A292155(n).

a(n) = A291718(n) - A292156(n).