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A059214 Square array T(k,n) = C(n-1,k) + Sum_{i=0..k} C(n,i) read by antidiagonals (k >= 1, n >= 1). 2
2, 2, 4, 2, 4, 6, 2, 4, 8, 8, 2, 4, 8, 14, 10, 2, 4, 8, 16, 22, 12, 2, 4, 8, 16, 30, 32, 14, 2, 4, 8, 16, 32, 52, 44, 16, 2, 4, 8, 16, 32, 62, 84, 58, 18, 2, 4, 8, 16, 32, 64, 114, 128, 74, 20, 2, 4, 8, 16, 32, 64, 126, 198, 186, 92, 22, 2, 4, 8, 16, 32, 64 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For k>1, gives maximal number of regions into which k-space can be divided by n hyper-spheres.

REFERENCES

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

LINKS

Table of n, a(n) for n=1..72.

FORMULA

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

EXAMPLE

Array begins

2 4 6 8 10 ...

2 4 8 14 22 ...

2 4 8 16 ...

CROSSREFS

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

Apart from left border, same as A059250. A178522 is probably the best version.

Sequence in context: A233763 A109526 A260723 * A091820 A171922 A140821

Adjacent sequences:  A059211 A059212 A059213 * A059215 A059216 A059217

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 15 2001

STATUS

approved

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Last modified October 18 06:17 EDT 2018. Contains 316304 sequences. (Running on oeis4.)