A292156 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 but no point symmetry.

0, 0, 0, 0, 0, 36, 0, 0, 168, 220, 0, 0, 524, 944, 1960, 0, 0, 1292, 2848, 6752, 15752, 0, 0, 2736, 7248, 20280, 55904, 120212, 0, 0, 5088, 15576, 48576, 156224, 378824, 1068008

Offset

1,6

Links

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

Formula

a(n) = A292153(n) - A291717(n) = A291718(n) - A292154(n).

Example

The triangle begins:
   0;
   0, 0;
   0, 0,   36;
   0, 0,  168,  220;
   0, 0,  524,  944,  1960;
   0, 0, 1292, 2848,  6752, 15752;
   0, 0, 2736, 7248, 20280, 55904, 120212;
.
The following configuration of 6 picked points from a 7X7 grid with a line (mirror) symmetry w.r.t. the line indicated by +++, but no point symmetry, is one of the T(7,6)=a(27)=55904 configurations with this property:
  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

Crossrefs

Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292153, A292154, A292155.

Sequence in context: A023929 A010113 A167264 * A265489 A262795 A309379

Adjacent sequences: A292153 A292154 A292155 * A292157 A292158 A292159

Keyword

nonn,tabl,more

Author

Hugo Pfoertner, Sep 17 2017

Status

approved