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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. 9
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 18:56 EDT 2019. Contains 328197 sequences. (Running on oeis4.)