A292153 - OEIS

%I #13 Sep 20 2017 05:08:54

%S 1,4,6,9,36,44,16,120,192,388,25,300,596,1658,2138,36,630,1436,5121,

%T 7216,22328,49,1176,3024,13180,21756,80192,126616,64,2016,5568,29112,

%U 51616,230784,394504,1409328

%N 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.

%C The "or" is inclusive, i.e. configurations that have both types of symmetry simultaneously (counted separately in A292154) are included.

%F a(n) = A090642(n) - A292152(n) = A292154(n) + A292155(n) + A292156(n).

%e The triangle begins:

%e    1;

%e    4,    6;

%e    9,   36,   44;

%e   16,  120,  192,   388;

%e   25,  300,  596,  1658,  2138;

%e   36,  630, 1436,  5121,  7216, 22328;

%e   49, 1176, 3024, 13180, 21756, 80192, 126616;

%e .

%e 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.

%e   0 0 0 0

%e   X 0 0 0

%e   0 X 0 0

%e   0 0 X 0

%Y Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292154, A292155, A292156.

%K nonn,tabl

%O 1,2

%A _Hugo Pfoertner_, Sep 17 2017