%I A046127
%S A046127 0,2,4,8,16,30,52,84,128,186,260,352,464,598,756,940,1152,1394,1668,
%T A046127 1976,2320,2702,3124,3588,4096,4650,5252,5904,6608,7366,8180,9052,
%U A046127 9984,10978,12036,13160,14352,15614,16948,18356,19840,21402,23044
%N A046127 Maximal number of regions into which space can be divided by n spheres.
%C A046127 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
%D A046127 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 73, Problem 4.
%D A046127 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)
%H A046127 T. D. Noe, <a href="b046127.txt">Table of n, a(n) for n=0..1000</a>
%H A046127 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SpaceDivisionbySpheres.html">Link to a section of The World of Mathematics.</
               a>
%F A046127 a(n)=n(n^2-3n+8)/3 (n>0).
%F A046127 n hyperspheres divide R^k into at most C(n-1, k) + Sum_{i=0..k} C(n, 
               i) regions.
%Y A046127 Cf. A014206 (dim 2), A046127 (dim 3), A059173 (dim 4), A059174 (dim 5). 
               See also A000124, A000125. A row of A059250.
%Y A046127 Sequence in context: A054154 A018469 A098904 this_sequence A075529 A005305 
               A125548
%Y A046127 Adjacent sequences: A046124 A046125 A046126 this_sequence A046128 A046129 
               A046130
%K A046127 nonn,easy,nice
%O A046127 0,2
%A A046127 Eric Weisstein (eric(AT)weisstein.com)