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A274818 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. 4

%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

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Last modified January 22 16:37 EST 2020. Contains 331152 sequences. (Running on oeis4.)