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 A059214 Square array T(k,n) = C(n-1,k) + Sum_{i=0..k} C(n,i) read by antidiagonals (k >= 1, n >= 1). 2

%I

%S 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,

%T 8,16,32,52,44,16,2,4,8,16,32,62,84,58,18,2,4,8,16,32,64,114,128,74,

%U 20,2,4,8,16,32,64,126,198,186,92,22,2,4,8,16,32,64

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

%C For k>1, gives maximal number of regions into which k-space can be divided by n hyper-spheres.

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

%F n hyperspheres divide R^k into at most C(n-1, k) + Sum_{i=0..k} C(n, i) regions.

%e Array begins

%e 2 4 6 8 10 ...

%e 2 4 8 14 22 ...

%e 2 4 8 16 ...

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

%Y Apart from left border, same as A059250. A178522 is probably the best version.

%K nonn,tabl

%O 1,1

%A _N. J. A. Sloane_, Feb 15 2001

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