A061559 Array read by antidiagonals: T(k,d) = number of different hyperplanes in d-space with integer coefficients in set {-k,...,-1,0,1,...,k}.

3, 7, 12, 15, 48, 39, 23, 144, 271, 120, 39, 288, 1119, 1440, 363, 47, 576, 2927, 8160, 7447, 1092, 71, 864, 6927, 27840, 58095, 37968, 3279, 87, 1440, 12767, 78720, 257543, 409584, 192031, 9840, 111, 2016, 23759, 175680, 877239, 2351328, 2875839

Offset: 1

Author

Carlos A.S Felgueiras (casf(AT)fe.up.pt), Jan 16 2004

Keywords

• nonn
• tabl

Comments

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.

Examples

			Array begins:
3 12 39 120 363 ...
7 48 271 1440 7447 ...
15 144 1119 8160 58095 ...
23 288 2927 27840 257543 ...
39 576 6927 78720 877239 ...
		

Crossrefs

Cf. A018805, A071778.