cp's OEIS Frontend

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.

%I A252158 #82 Jun 16 2017 22:26:40
%S A252158 1,2,1,11,2,1,155,15,2,1
%N 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.
%C A252158 Consider the rules for the arrangements of n circles described in A250001.
%C A252158 Right border gives A000012. - _Omar E. Pol_, Aug 09 2015
%C A252158 From _Omar E. Pol_, May 21 2017: (Start)
%C A252158 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.
%C A252158 T(4,2) = 15 includes the arrangement mentioned above.
%C A252158 1 together with the first column gives A287149.
%C A252158 For another version see A285996. (End) (Comment clarified on Jun 15 2017.)
%e A252158 Triangle begins:
%e A252158 1;
%e A252158 2,   1;
%e A252158 11,  2,   1;
%e A252158 155, 15,  2,  1;
%Y A252158 Row sums give A250001, n >= 1.
%Y A252158 Cf. A249752, A285996 (another version), A287149.
%K A252158 nonn,tabl,hard,more
%O A252158 1,2
%A A252158 _Omar E. Pol_, Dec 14 2014
%E A252158 Clarified definition and a(7)-a(10) added by _Omar E. Pol_, May 21 2017
%E A252158 Clarified definition and comment by _Omar E. Pol_, Jun 15 2017