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A059250 Square array read by antidiagonals: T(k,n) = C(n-1, k) + Sum_{i=0..k} C(n, i), k >=1, n >= 0. 5
1, 1, 2, 1, 2, 4, 1, 2, 4, 6, 1, 2, 4, 8, 8, 1, 2, 4, 8, 14, 10, 1, 2, 4, 8, 16, 22, 12, 1, 2, 4, 8, 16, 30, 32, 14, 1, 2, 4, 8, 16, 32, 52, 44, 16, 1, 2, 4, 8, 16, 32, 62, 84, 58, 18, 1, 2, 4, 8, 16, 32, 64, 114, 128, 74, 20, 1, 2, 4, 8, 16, 32, 64, 126, 198, 186, 92, 22, 1, 2, 4, 8, 16, 32, 64 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

T(k,n) = maximal number of regions into which k-space can be divided by n hyper-spheres (k >= 1, n >= 0).

For all fixed k, the sequences T(k,n) are complete. [Frank M Jackson, Jan 26, 2012]

REFERENCES

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

LINKS

Table of n, a(n) for n=1..85.

EXAMPLE

Array begins

1 2 4 6 8 10 12 ...

1 2 4 8 14 22 ...

1 2 4 8 16 ...

MATHEMATICA

getvalue[n_, k_] := If[n==0, 1, Binomial[n-1, k]+Sum[Binomial[n, i], {i, 0, k}]]; lexicographicLattice[{dim_, maxHeight_}] := Flatten[Array[Sort@Flatten[(Permutations[#1] &) /@     IntegerPartitions[#1 + dim - 1, {dim}], 1] &, maxHeight], 1]; pairs=lexicographicLattice[{2, 13}]-1; Table[getvalue[First[pairs[[j]]], Last[pairs[[j]]]+1], {j, 1, Length[pairs]}] (* Frank M Jackson, Mar 16 2013 *)

CROSSREFS

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

Apart from border, same as A059214. If the k=0 row is included, same as A178522.

Sequence in context: A141539 A243851 A168266 * A131074 A059268 A123937

Adjacent sequences:  A059247 A059248 A059249 * A059251 A059252 A059253

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 15 2001

EXTENSIONS

Corrected and edited by N. J. A. Sloane, Aug 31 2011, following a suggestion from Frank M. Jackson.

STATUS

approved

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Last modified December 20 23:03 EST 2014. Contains 252290 sequences.