

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.


5



1, 0, 2, 1, 0, 0, 4, 4, 2, 1, 3, 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.
Note that the sum of the 4th row must be equal to A250001(4) = 173.


LINKS

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


FORMULA

T(n,k) = A274819(n,k)/k.


EXAMPLE

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.


CROSSREFS

Sum of nth row = A250001(n).
First differs from A274776 at a(10).
Cf. A250001, A249752, A252158, A261070, A274819, A274823.
Sequence in context: A192396 A094449 A274776 * A136129 A278213 A034093
Adjacent sequences: A274774 A274775 A274776 * A274778 A274779 A274780


KEYWORD

nonn,tabf,hard,more


AUTHOR

Omar E. Pol, Jul 06 2016


STATUS

approved



