

A059214


Square array T(k,n) = C(n1,k) + Sum_{i=0..k} C(n,i) read by antidiagonals (k >= 1, n >= 1).


3



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.
The maximum number of subsets of a set of n points in kspace that can be formed by intersecting it with a hyperplane.  Günter Rote, Dec 18 2018


REFERENCES

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


LINKS

Table of n, a(n) for n=1..72.
E. F. Harding, The number of partitions of a set of n points in k dimensions induced by hyperplanes, Proc. Edinburgh Math. Soc., 15 (1967), 285289.


FORMULA

a(n) = C(n1, k) + Sum_{i=0..k} C(n, i).


EXAMPLE

Array begins
2 4 6 8 10 12 ...
2 4 8 14 22 32 ...
2 4 8 16 30 52 ...


CROSSREFS

Cf. A014206 (dim 2), A046127 (dim 3), A059173 (dim 4), A059174 (dim 5).
Equals twice A216274.
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,changed


AUTHOR

N. J. A. Sloane, Feb 15 2001


STATUS

approved



