This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A274819 #22 Jul 10 2016 22:56:03 %S A274819 1,0,4,3,0,0,12,16,10,6,21,0,0,0 %N A274819 Triangle read by rows: T(n,k) = total number of regions in all arrangements of n circles in the affine plane forming k regions, excluding the regions that do not belong to the circles. %C A274819 In other words: not counting the regions between circles. %C A274819 Consider the arrangements of n circles described in A250001. %F A274819 T(n,k) = k*A274777(n,k). %e A274819 Triangle begins: %e A274819 1; %e A274819 0, 4, 3; %e A274819 0, 0, 12, 16, 10, 6, 21; %e A274819 0, 0, 0, ... %e A274819 ... %e A274819 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*5 = 10. %e A274819 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*6 = 6. %e A274819 Of course, there is a right triangle of all zeros starting from the second row. %Y A274819 Row sums give A274823(n). %Y A274819 First differs from A274818 at a(10). %Y A274819 Cf. A250001, A274777. %K A274819 nonn,tabf,hard,more %O A274819 1,3 %A A274819 _Omar E. Pol_, Jul 07 2016