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A046127 Maximal number of regions into which space can be divided by n spheres. 6
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; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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 Janjic, Dec 28 2007

REFERENCES

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)

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Space Division by Spheres.

FORMULA

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.

a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: 2*x*(1-2*x+2*x^2)/(1-x)^4. [Colin Barker, Jan 28 2012]

MATHEMATICA

Join[{0}, Table[n (n^2-3n+8)/3, {n, 50}]]  (* Harvey P. Dale, Apr 21 2011 *)

CROSSREFS

Cf. A014206 (dim 2), A046127 (dim 3), A059173 (dim 4), A059174 (dim 5). See also A000124, A000125. A row of A059250.

Sequence in context: A018469 A098904 A248846 * A271480 A226454 A075529

Adjacent sequences:  A046124 A046125 A046126 * A046128 A046129 A046130

KEYWORD

nonn,easy,nice

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified August 20 03:34 EDT 2017. Contains 290823 sequences.