

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



