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A274776
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Irregular triangle read by rows: T(n,k) = number of arrangements of n circles in the affine plane forming k regions, including the regions that do not belong to the circles.
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5
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1, 0, 2, 1, 0, 0, 4, 4, 2, 0, 4, 0, 0, 0
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OFFSET
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1,3
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COMMENTS
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Consider the arrangements of n circles described in A250001.
Note that the sum of the 4th row must be equal to A250001(4) = 173.
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
0, 2, 1;
0, 0, 4, 4, 2, 0, 4;
0, 0, 0, ...
...
For n = 3 and k = 5 there are 2 arrangements of 3 circles in the affine plane forming 5 regions, including the regions that do not belong to the circles, so T(3,5) = 2.
For n = 3 and k = 6 there are no arrangements of 3 circles in the affine plane forming 6 regions, including the regions that do not belong to the circles, so T(3,6) = 0.
Of course, there is a right triangle of all zeros starting from the second row.
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CROSSREFS
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First differs from A274777 at a(10).
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KEYWORD
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nonn,tabf,hard,more
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AUTHOR
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STATUS
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approved
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