|
|
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.
|
|
7
|
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Consider the rules for the arrangements of n circles described in A250001.
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.)
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins:
1;
2, 1;
11, 2, 1;
155, 15, 2, 1;
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
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
|
|
STATUS
|
approved
|
|
|
|