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