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 A046127 Maximal number of regions into which space can be divided by n spheres. 7
 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 n hyperspheres divide R^k into at most C(n-1, k) + Sum_{i=0..k} C(n, i) regions. a(n) = n*(n^2 - 3*n + 8)/3 (n >= 0). From Philip C. Ritchey, Dec 09 2017: (Start) The above identity proved as closed form of the following summation and its corresponding recurrence relation: a(n) = Sum_{i=1..n} (i*(i-3) + 4). a(n) = a(n-1) + n*(n-3) + 4, a(0) = 0. (End) From Colin Barker, Jan 28 2012: (Start) 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. (End) MATHEMATICA Join[{0}, Table[n (n^2-3n+8)/3, {n, 50}]]  (* Harvey P. Dale, Apr 21 2011 *) PROG (Python) def a(n): ....return n*(n**2 - 3*n + 8)//3 # Philip C. Ritchey, Dec 10 2017 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 STATUS approved

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Last modified October 18 00:21 EDT 2019. Contains 328135 sequences. (Running on oeis4.)