|
%I #2 Feb 19 2004 03:00:00
%S 3,7,12,15,48,39,23,144,271,120,39,288,1119,1440,363,47,576,2927,8160,
%T 7447,1092,71,864,6927,27840,58095,37968,3279,87,1440,12767,78720,
%U 257543,409584,192031,9840,111,2016,23759,175680,877239,2351328,2875839
%N Array read by antidiagonals: T(k,d) = number of different hyperplanes in d-space with integer coefficients in set {-k,...,-1,0,1,...,k}.
%C The number of hyperplanes is T(k,d)=Sum(binomial(d,i)2^(d-i-1)(2*M(d+1-i,k)+M(d-i,k)),i=0..d-1) or T(k,d)=(1/2)*Sum(binomial(n,i)2^(n-i)M(n-i,k),i=0..n-1)-1, with n=d+1, where M(n,k) is the number of n-tuples (a,b,...) with 1<=a,b,...<=k and gcd(a,b,...)=1 T(1,d) is A029858 for n>=2.
%e Array begins:
%e 3 12 39 120 363 ...
%e 7 48 271 1440 7447 ...
%e 15 144 1119 8160 58095 ...
%e 23 288 2927 27840 257543 ...
%e 39 576 6927 78720 877239 ...
%Y Cf. A018805, A071778.
%K nonn,tabl
%O 1,1
%A Carlos A.S Felgueiras (casf(AT)fe.up.pt), Jan 16 2004
|
