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A059174 Maximal number of regions into which 5-space can be divided by n hyper-spheres. 7
1, 2, 4, 8, 16, 32, 64, 126, 240, 438, 764, 1276, 2048, 3172, 4760, 6946, 9888, 13770, 18804, 25232, 33328, 43400, 55792, 70886, 89104, 110910, 136812, 167364, 203168, 244876, 293192, 348874, 412736, 485650, 568548, 662424, 768336 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 73, Problem 4.

LINKS

Table of n, a(n) for n=0..36.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

n hyperspheres divide R^k into at most C(n-1, k) + Sum_{i=0..k} C(n, i) regions.

G.f.: (x^6+3*x^4-6*x^3+7*x^2-4*x+1)/(x-1)^6. [Colin Barker, Oct 06 2012]

PROG

(PARI) a(n) = binomial(n-1, 5) + sum(i=0, 5, binomial(n, i)); \\ Michel Marcus, Jan 29 2016

CROSSREFS

Cf. A014206 (dim 2), A046127 (dim 3), A059173 (dim 4), A059174 (dim 5).

Sequence in context: A208743 A247213 A069050 * A258585 A235701 A054044

Adjacent sequences:  A059171 A059172 A059173 * A059175 A059176 A059177

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 15 2001

STATUS

approved

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Last modified February 20 15:02 EST 2018. Contains 299380 sequences. (Running on oeis4.)