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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.

%I A292153 #13 Sep 20 2017 05:08:54
%S A292153 1,4,6,9,36,44,16,120,192,388,25,300,596,1658,2138,36,630,1436,5121,
%T A292153 7216,22328,49,1176,3024,13180,21756,80192,126616,64,2016,5568,29112,
%U A292153 51616,230784,394504,1409328
%N 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.
%C A292153 The "or" is inclusive, i.e. configurations that have both types of symmetry simultaneously (counted separately in A292154) are included.
%F A292153 a(n) = A090642(n) - A292152(n) = A292154(n) + A292155(n) + A292156(n).
%e A292153 The triangle begins:
%e A292153    1;
%e A292153    4,    6;
%e A292153    9,   36,   44;
%e A292153   16,  120,  192,   388;
%e A292153   25,  300,  596,  1658,  2138;
%e A292153   36,  630, 1436,  5121,  7216, 22328;
%e A292153   49, 1176, 3024, 13180, 21756, 80192, 126616;
%e A292153 .
%e A292153 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 A292153   0 0 0 0
%e A292153   X 0 0 0
%e A292153   0 X 0 0
%e A292153   0 0 X 0
%Y A292153 Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292154, A292155, A292156.
%K A292153 nonn,tabl
%O A292153 1,2
%A A292153 _Hugo Pfoertner_, Sep 17 2017