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A287152 Number T(n,k) of tilings of a 2 X n X n box using k bricks of shape 2 X 1 X 1 and 2*(n^2-k) bricks of shape 1 X 1 X 1; triangle T(n,k), n>=0, 0<=k<=n^2, read by rows.

%I A287152 #9 May 20 2017 20:07:18
%S A287152 1,1,1,1,12,42,44,9,1,33,436,2984,11434,24766,29180,16984,3993,229,1,
%T A287152 64,1816,30208,328214,2456736,13022504,49492032,135062729,262610832,
%U A287152 357580896,331384336,200032432,73483328,14707328,1308928,32000,1,105,5112,153364,3178256
%N A287152 Number T(n,k) of tilings of a 2 X n X n box using k bricks of shape 2 X 1 X 1 and 2*(n^2-k) bricks of shape 1 X 1 X 1; triangle T(n,k), n>=0, 0<=k<=n^2, read by rows.
%H A287152 Alois P. Heinz, <a href="/A287152/b287152.txt">Rows n = 0..8, flattened</a>
%e A287152 Triangle T(n,k) begins:
%e A287152 1;
%e A287152 1,  1;
%e A287152 1, 12,  42,   44,     9;
%e A287152 1, 33, 436, 2984, 11434, 24766, 29180, 16984, 3993, 229;
%Y A287152 Columns k=0-1 give: A000012, A051624.
%Y A287152 Row sums give A287153.
%Y A287152 T(n,n^2) gives A181205.
%K A287152 nonn,tabf
%O A287152 0,5
%A A287152 _Alois P. Heinz_, May 20 2017