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

1,2

Links

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

Formula

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

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

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

Example

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.

Sequence in context: A081614 A192220 A215477 * A291717 A303699 A292153

Adjacent sequences: A292151 A292152 A292153 * A292155 A292156 A292157

Keyword

nonn,tabl,more

Author

Hugo Pfoertner, Sep 17 2017

Status

approved