A274777 Irregular triangle read by rows: T(n,k) = number of arrangements of n circles in the affine plane forming k regions, excluding the regions that do not belong to the circles.

1, 0, 2, 1, 0, 0, 4, 4, 2, 1, 3, 0, 0, 0

Offset: 1

Author

Omar E. Pol, Jul 06 2016

Keywords

• nonn
• tabf
• hard
• more

Comments

In other words: not counting the regions between circles.

Consider the arrangements of n circles described in A250001.

Note that the sum of the 4th row must be equal to A250001(4) = 173.

Examples

			Triangle begins:
1;
0, 2, 1;
0, 0, 4, 4, 2, 1, 3;
0, 0, 0, ...
...
For n = 3 and k = 5 there are 2 arrangements of 3 circles in the affine plane forming 5 regions, excluding the regions that do not belong to the circles, so T(3,5) = 2.
For n = 3 and k = 6 there is only one arrangement of 3 circles in the affine plane forming 6 regions, excluding the regions that do not belong to the circles, so T(3,6) = 1.
Of course, there is a right triangle of all zeros starting from the second row.
		

Crossrefs

Sum of n-th row = A250001(n).

First differs from A274776 at a(10).

Cf. A250001, A249752, A252158, A261070, A274819, A274823.

Formula

T(n,k) = A274819(n,k)/k.