

A059214


Square array T(k,n) = C(n1,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 kspace can be divided by n hyperspheres.


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(n1, 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



