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Search: id:A059250
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| A059250 |
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Square array T(k,n) = maximal number of regions into which k-space can be divided by n hyper-spheres (k >= 1, n >= 1). |
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+0
5
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| 1, 1, 2, 1, 2, 3, 1, 2, 4, 4, 1, 2, 4, 8, 5, 1, 2, 4, 8, 14, 6, 1, 2, 4, 8, 16, 22, 7, 1, 2, 4, 8, 16, 30, 32, 8, 1, 2, 4, 8, 16, 32, 52, 44, 9, 1, 2, 4, 8, 16, 32, 62, 84, 58, 10, 1, 2, 4, 8, 16, 32, 64, 114, 128, 74, 11, 1, 2, 4, 8, 16, 32, 64, 126, 198, 186, 92, 12, 1, 2, 4, 8, 16, 32, 64
(list; table; graph; listen)
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OFFSET
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1,3
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 73, Problem 4.
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FORMULA
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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
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Array begins
1 2 3 4 5 6 ...
1 2 4 8 14 22 ...
1 2 4 8 16 ...
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CROSSREFS
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Cf. A014206 (dim 2), A046127 (dim 3), A059173 (dim 4), A059174 (dim 5).
Apart from border, same as A059214.
Sequence in context: A163491 A080772 A145111 this_sequence A104795 A116925 A131879
Adjacent sequences: A059247 A059248 A059249 this_sequence A059251 A059252 A059253
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 15 2001
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