%I #13 Sep 20 2017 05:09:19
%S 0,0,0,0,0,36,0,0,168,220,0,0,524,944,1960,0,0,1292,2848,6752,15752,0,
%T 0,2736,7248,20280,55904,120212,0,0,5088,15576,48576,156224,378824,
%U 1068008
%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 line symmetry but no point symmetry.
%F a(n) = A292153(n) - A291717(n) = A291718(n) - A292154(n).
%e The triangle begins:
%e 0;
%e 0, 0;
%e 0, 0, 36;
%e 0, 0, 168, 220;
%e 0, 0, 524, 944, 1960;
%e 0, 0, 1292, 2848, 6752, 15752;
%e 0, 0, 2736, 7248, 20280, 55904, 120212;
%e .
%e The following configuration of 6 picked points from a 7X7 grid with a line (mirror) symmetry w.r.t. the line indicated by +++, but no point symmetry, is one of the T(7,6)=a(27)=55904 configurations with this property:
%e o o o o o o o
%e + X o X o o o
%e X + o o o X o
%e o o + o o o o
%e X o o + o o o
%e o o o o + o o
%e o X o o o + o
%Y Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292153, A292154, A292155.
%K nonn,tabl,more
%O 1,6
%A _Hugo Pfoertner_, Sep 17 2017
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