

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.


4



1, 0, 4, 3, 0, 0, 12, 16, 10, 6, 21, 0, 0, 0
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OFFSET

1,3


COMMENTS

In other words: not counting the regions between circles.
Consider the arrangements of n circles described in A250001.


LINKS

Table of n, a(n) for n=1..14.


FORMULA

T(n,k) = k*A274777(n,k).


EXAMPLE

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.


CROSSREFS

Row sums give A274823(n).
First differs from A274818 at a(10).
Cf. A250001, A274777.
Sequence in context: A019984 A187765 A274818 * A106646 A056969 A131106
Adjacent sequences: A274816 A274817 A274818 * A274820 A274821 A274822


KEYWORD

nonn,tabf,hard,more


AUTHOR

Omar E. Pol, Jul 07 2016


STATUS

approved



