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 A216274 Square array A(n,k) = maximal number of regions into which k-space can be divided by n hyperplanes (k >= 1, n >= 0), read by antidiagonals. 1
 1, 1, 2, 1, 2, 3, 1, 2, 4, 4, 1, 2, 4, 7, 5, 1, 2, 4, 8, 11, 6, 1, 2, 4, 8, 15, 16, 7, 1, 2, 4, 8, 16, 26, 22, 8, 1, 2, 4, 8, 16, 31, 42, 29, 9, 1, 2, 4, 8, 16, 32, 57, 64, 37, 10, 1, 2, 4, 8, 16, 32, 63, 99, 93, 46, 11, 1, 2, 4, 8, 16, 32, 64, 120, 163, 130, 56, 12 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For all fixed k, the sequences A(n,k) are "complete" (sic). This array is similar to A145111 with first variation at 34th term. LINKS Table of n, a(n) for n=0..77. Wikipedia, "Complete" sequence. [Wikipedia calls a sequence "complete" (sic) if every positive integer is a sum of distinct terms. This name is extremely misleading and should be avoided. - N. J. A. Sloane, May 20 2023] FORMULA A(k,n) = Sum_{i=0..k} C(n, i), k >=1, n >= 0. EXAMPLE Square array A(n,k) begins: 1, 1, 1, 1, 1, 1, ... 2, 2, 2, 2, 2, 2, ... 3, 4, 4, 4, 4, 4, ... 4, 7, 8, 8, 8, 8, ... 5, 11, 15, 16, 16, 16, ... 6, 16, 26, 31, 32, 32, ... So the maximal number of pieces into which a cube can be divided after 5 planar cuts is A(5,3) = 26. MATHEMATICA getvalue[n_, 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, 12}]-1; Table[getvalue[First[pairs[[j]]], Last[pairs[[j]]]+1], {j, 1, Length[pairs]}] CROSSREFS Cf. A000124, A000125, A059214. Sequence in context: A163491 A080772 A259324 * A145111 A104795 A347570 Adjacent sequences: A216271 A216272 A216273 * A216275 A216276 A216277 KEYWORD nonn,tabl AUTHOR Frank M Jackson, Mar 16 2013 EXTENSIONS Edited by N. J. A. Sloane, May 20 2023 STATUS approved

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Last modified February 27 08:11 EST 2024. Contains 370367 sequences. (Running on oeis4.)