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Triangle read by rows: T(n,k) is the number of n X n binary matrices with k=0..n^2 ones forming a polyomino, under action of dihedral group of the square D_4.
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%I #30 Jul 05 2020 12:52:38

%S 0,0,1,0,1,1,1,1,0,3,2,5,6,10,8,7,3,1,0,3,4,8,17,33,68,119,195,261,

%T 300,257,169,66,20,3,1,0,6,6,16,32,82,189,470,1076,2422,5010,9732,

%U 17145,27399,38680,47560,49325,41872,27864,14095,5280,1470,302,48,6,1

%N Triangle read by rows: T(n,k) is the number of n X n binary matrices with k=0..n^2 ones forming a polyomino, under action of dihedral group of the square D_4.

%C By forming a polyomino it is meant that there is at least one 1 and that all the 1's are connected horizontally or vertically.

%H Jean-Luc Manguin, <a href="/A331462/b331462.txt">Table of n, a(n) for n = 0..97</a>

%H Jean-Luc Manguin, <a href="/A331462/a331462.pdf">Illustration of a(3) and comparison with A268416</a>

%e Triangle begins:

%e 0;

%e 0, 1;

%e 0, 1, 1, 1, 1;

%e 0, 3, 2, 5, 6, 10, 8, 7, 3, 1;

%e 0, 3, 4, 8, 17, 33, 68, 119, 195, 261, 300, 257, 169, 66, 20, 3, 1;

%e ...

%Y Cf. A054252, A268416.

%K nonn,tabf

%O 0,10

%A _Jean-Luc Manguin_, Jan 17 2020