|
%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
|
