A285996 Triangle read by rows, 1<=k<=n, T(n,k) = number of arrangements of n circles in the affine plane having k separated islands.

1, 2, 1, 11, 2, 1, 156, 14, 2, 1

Offset: 1

Author

Omar E. Pol, May 21 2017

Keywords

• nonn
• tabl
• hard
• more

Comments

Consider the rules for the arrangements of n circles described in A250001.

Note that T(4,1) = 156 includes the arrangement of 4 circles in which there is a little circle that is surrounded by the union of three solid circles, because the little circle is an inland island, or lake island, which does not count. So there is only one separated island. Hence T(4,2) = 14 does not include the mentioned arrangement.

Question: is 1 together with the first column of the triangle the same as A275923?

Examples

			Triangle begins:
1;
2,   1;
11,  2,  1;
156, 14, 2, 1;
		

Crossrefs

Another version of A252158.

Row sums give A250001, n >= 1.

Right border gives A000012.

Cf. A249752, A275923.