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.

1, 0, 4, 3, 0, 0, 12, 16, 10, 0, 28, 0, 0, 0

Offset: 1

Author

Omar E. Pol, Jul 07 2016

Keywords

• nonn
• tabf
• hard
• more

Comments

Consider the arrangements of n circles described in A250001.

Examples

			Triangle begins:
1;
0, 4,  3;
0, 0, 12, 16, 10, 0, 28;
0, 0,  0, ...
...
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.
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.
Of course, there is a right triangle of all zeros starting from the second row.
		

Crossrefs

Row sums give A274822.

First differs from A274819 at a(10).

Cf. A250001, A274776.

Formula

T(n,k) = k*A274776(n,k).