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A261070
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Irregular triangle read by rows: T(n,k) is the number of arrangements of n circles with 2k intersections (using the same rules as A250001).
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6
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OFFSET
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0,3
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COMMENTS
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Length of n-th row: 1 + (n-1)n/2 (for a configuration for T(n,(n-1)n/2), consider n circles of radius 1 and centers at (k/n,0) for 1<=k<=n).
The generating function down the column k=1 is 1+z^2 *C^2(z) *[C^2(z)+C(z^2)]/ (2*[1-z*C(z)]) = 1+ z^2 +4*z^3 +15*z^4+ 50*z^5+...where C(z) = 1+z+2*z^2+4*z^3+... is the g.f. of A000081 divided by z; eq. (78) in arXiv:1603.00077. - R. J. Mathar, Mar 05 2016
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LINKS
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FORMULA
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EXAMPLE
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n\k 0 1 2 3 4 5 6
0 1
1 1
2 2 1
3 4 4 2 4
4 9 15 . . . . .
5 20 .
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CROSSREFS
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KEYWORD
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nonn,more,tabf
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AUTHOR
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STATUS
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approved
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