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A059214
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Square array T(k,n) = C(n-1,k) + Sum_{i=0..k} C(n,i) read by antidiagonals (k >= 1, n >= 1).
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2
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2, 2, 4, 2, 4, 6, 2, 4, 8, 8, 2, 4, 8, 14, 10, 2, 4, 8, 16, 22, 12, 2, 4, 8, 16, 30, 32, 14, 2, 4, 8, 16, 32, 52, 44, 16, 2, 4, 8, 16, 32, 62, 84, 58, 18, 2, 4, 8, 16, 32, 64, 114, 128, 74, 20, 2, 4, 8, 16, 32, 64, 126, 198, 186, 92, 22, 2, 4, 8, 16, 32, 64
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For k>1, gives maximal number of regions into which k-space can be divided by n hyper-spheres.
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 73, Problem 4.
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FORMULA
| n hyperspheres divide R^k into at most C(n-1, k) + Sum_{i=0..k} C(n, i) regions.
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EXAMPLE
| Array begins
2 4 6 8 10 ...
2 4 8 14 22 ...
2 4 8 16 ...
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CROSSREFS
| Cf. A014206 (dim 2), A046127 (dim 3), A059173 (dim 4), A059174 (dim 5).
Apart from left border, same as A059250. A178522 is probably the best version.
Sequence in context: A060609 A205138 A109526 * A091820 A171922 A140821
Adjacent sequences: A059211 A059212 A059213 * A059215 A059216 A059217
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 15 2001
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