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Search: id:A046127
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| A046127 |
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Maximal number of regions into which space can be divided by n spheres. |
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+0
6
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| 0, 2, 4, 8, 16, 30, 52, 84, 128, 186, 260, 352, 464, 598, 756, 940, 1152, 1394, 1668, 1976, 2320, 2702, 3124, 3588, 4096, 4650, 5252, 5904, 6608, 7366, 8180, 9052, 9984, 10978, 12036, 13160, 14352, 15614, 16948, 18356, 19840, 21402, 23044
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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If Y is a 2-subset of an n-set X then, for n>=2, a(n-2) is equal to the number of 2-subsets and 4-subsets of X having exactly one element in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 73, Problem 4.
A. M. Yaglom and I. M. Yaglom: Challenging Mathematical Problems with Elementary Solutions. Vol. I. Combinatorial Analysis and Probability Theory. New York: Dover Publications, Inc., 1987, p. 13, #45 (First published: San Francisco: Holden-Day, Inc., 1964)
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n)=n(n^2-3n+8)/3 (n>0).
n hyperspheres divide R^k into at most C(n-1, k) + Sum_{i=0..k} C(n, i) regions.
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CROSSREFS
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Cf. A014206 (dim 2), A046127 (dim 3), A059173 (dim 4), A059174 (dim 5). See also A000124, A000125. A row of A059250.
Sequence in context: A054154 A018469 A098904 this_sequence A075529 A005305 A125548
Adjacent sequences: A046124 A046125 A046126 this_sequence A046128 A046129 A046130
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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