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A059250
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Square array read by antidiagonals: T(k,n) = C(n-1, k) + Sum_{i=0..k} C(n, i), k >=1, n >= 0.
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5
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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
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OFFSET
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1,3
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COMMENTS
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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]
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 73, Problem 4.
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LINKS
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Table of n, a(n) for n=1..85.
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EXAMPLE
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Array begins
1 2 4 6 8 10 12 ...
1 2 4 8 14 22 ...
1 2 4 8 16 ...
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MATHEMATICA
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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 *)
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CROSSREFS
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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: A174843 A141539 A168266 * A131074 A059268 A123937
Adjacent sequences: A059247 A059248 A059249 * A059251 A059252 A059253
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KEYWORD
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nonn,tabl
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AUTHOR
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N. J. A. Sloane, Feb 15 2001
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EXTENSIONS
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Corrected and edited by N. J. A. Sloane, Aug 31 2011, following a suggestion from Frank M. Jackson.
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STATUS
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approved
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