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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 18:08 EDT 2018. Contains 316401 sequences. (Running on oeis4.)