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A292154 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 both a point symmetry and a line symmetry.

%I A292154 #12 Sep 20 2017 05:09:02
%S A292154 1,4,6,9,36,8,16,120,24,56,25,300,72,186,50,36,630,144,473,128,648,49,
%T A292154 1176,288,1024,320,1660,728,64,2016,480,1952,608,3560,1520,7326
%N A292154 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 both a point symmetry and a line symmetry.
%F A292154 a(n) = A292153(n) - A292155(n) - A292156(n).
%F A292154 a(n) = A291717(n) - A292155(n).
%F A292154 a(n) = A291718(n) - A292156(n).
%e A292154 The triangle begins:
%e A292154    1;
%e A292154    4,    6;
%e A292154    9,   36,   8;
%e A292154   16,  120,  24,   56;
%e A292154   25,  300,  72,  186,  50;
%e A292154   36,  630, 144,  473, 128,  648;
%e A292154   49, 1176, 288, 1024, 320, 1660,  728;
%e A292154   64, 2016, 480, 1952, 608, 3560, 1520, 7326;
%e A292154 .
%e A292154   o o o o o o
%e A292154   X o o X o o
%e A292154   o o o o o o
%e A292154   X o o X o o
%e A292154   o o o o o o
%e A292154   X o o X o o
%e A292154 is one of the T(6,6)=a(21)=648 configurations with both types of symmetry.
%e A292154 .
%e A292154   o o X o o o
%e A292154   o X o o o o
%e A292154   o o o X o o
%e A292154   o o o o o X
%e A292154   o o o o X o
%e A292154   o o o o o o
%e A292154 is one of the T(6,5)=a(20)=128 configurations with both types of symmetry.
%Y A292154 Cf. A090642, A098485, A098487, A291716, A291717, A291718, A292152, A292153, A292155, A292156.
%K A292154 nonn,tabl,more
%O A292154 1,2
%A A292154 _Hugo Pfoertner_, Sep 17 2017