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%I #42 Apr 18 2019 04:43:03
%S 1,0,2,1,0,0,4,4,2,1,3,0,0,0
%N 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.
%C In other words: not counting the regions between circles.
%C Consider the arrangements of n circles described in A250001.
%C Note that the sum of the 4th row must be equal to A250001(4) = 173.
%F T(n,k) = A274819(n,k)/k.
%e Triangle begins:
%e 1;
%e 0, 2, 1;
%e 0, 0, 4, 4, 2, 1, 3;
%e 0, 0, 0, ...
%e ...
%e 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.
%e 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.
%e Of course, there is a right triangle of all zeros starting from the second row.
%Y Sum of n-th row = A250001(n).
%Y First differs from A274776 at a(10).
%Y Cf. A250001, A249752, A252158, A261070, A274819, A274823.
%K nonn,tabf,hard,more
%O 1,3
%A _Omar E. Pol_, Jul 06 2016
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