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

1,2

Links

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

Example

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.

Sequence in context: A227553 A108270 A019161 * A137026 A090938 A058229

Adjacent sequences: A291715 A291716 A291717 * A291719 A291720 A291721

Keyword

nonn,tabl,more

Author

Hugo Pfoertner, Sep 08 2017

Status

approved