

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.


9



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
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OFFSET

1,2


LINKS



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



KEYWORD



AUTHOR



STATUS

approved



