%I
%S 1,0,4,3,0,0,12,16,10,0,28,0,0,0
%N Triangle read by rows: T(n,k) = total number of regions in all arrangements of n circles in the affine plane forming k regions, including the regions that do not belong to the circles.
%C Consider the arrangements of n circles described in A250001.
%F T(n,k) = k*A274776(n,k).
%e Triangle begins:
%e 1;
%e 0, 4, 3;
%e 0, 0, 12, 16, 10, 0, 28;
%e 0, 0, 0, ...
%e ...
%e For n = 3 and k = 5 there are 2 arrangements of 3 circles in the affine plane forming 5 regions, including the regions that do not belong to the circles, so T(3,5) = 2*5 = 10.
%e For n = 3 and k = 6 there are no arrangements of 3 circles in the affine plane forming 6 regions, including the regions that do not belong to the circles, so T(3,6) = 0*5 = 0.
%e Of course, there is a right triangle of all zeros starting from the second row.
%Y Row sums give A274822.
%Y First differs from A274819 at a(10).
%Y Cf. A250001, A274776.
%K nonn,tabf,hard,more
%O 1,3
%A _Omar E. Pol_, Jul 07 2016
