A274777
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.
Original entry on oeis.org
1, 0, 2, 1, 0, 0, 4, 4, 2, 1, 3, 0, 0, 0
Offset: 1
Triangle begins:
1;
0, 2, 1;
0, 0, 4, 4, 2, 1, 3;
0, 0, 0, ...
...
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.
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.
Of course, there is a right triangle of all zeros starting from the second row.
First differs from
A274776 at a(10).
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.
Original entry on oeis.org
1, 0, 4, 3, 0, 0, 12, 16, 10, 6, 21, 0, 0, 0
Offset: 1
Triangle begins:
1;
0, 4, 3;
0, 0, 12, 16, 10, 6, 21;
0, 0, 0, ...
...
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.
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.
Of course, there is a right triangle of all zeros starting from the second row.
First differs from
A274818 at a(10).
A274822
Total number of regions in all arrangements of n circles in the affine plane, including the regions that do not belong to the circles.
Original entry on oeis.org
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