A252158 Triangle read by rows, 1 <= k <= n, T(n,k) = number of arrangements of n circles in the affine plane having k solid regions in which the union of solid circles is connected.

1, 2, 1, 11, 2, 1, 155, 15, 2, 1

Offset: 1

Author

Omar E. Pol, Dec 14 2014

Keywords

• nonn
• tabl
• hard
• more

Comments

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

Right border gives A000012. - Omar E. Pol, Aug 09 2015

From Omar E. Pol, May 21 2017: (Start)

Note that T(4,1) = 155 does not include the arrangement of four circles in which there is a central circle that is surrounded by the union of three circles, because in that arrangement there are two solid regions, not one. The smallest solid region is formed by the central solid circle. The largest solid region is formed by the union of three solid circles.

T(4,2) = 15 includes the arrangement mentioned above.

1 together with the first column gives A287149.

For another version see A285996. (End) (Comment clarified on Jun 15 2017.)

Examples

			Triangle begins:
1;
2,   1;
11,  2,   1;
155, 15,  2,  1;
		

Crossrefs

Row sums give A250001, n >= 1.

Cf. A249752, A285996 (another version), A287149.

Extensions

Clarified definition and a(7)-a(10) added by Omar E. Pol, May 21 2017

Clarified definition and comment by Omar E. Pol, Jun 15 2017