A103658 Number of configurations of 4 distinct points chosen from an (n+1) X (n+1) X (n+1) lattice cube resulting in objects with volume=0.

12, 2918, 64576, 673943, 4058656, 19462319, 70636336, 224091378, 621046332, 1573877652, 3582064304, 3582064304, 15781332296

Offset: 1

Author

Hugo Pfoertner, Feb 14 2005

Keywords

• hard
• more
• nonn

Examples

			a(1)=12 because the 6 faces and 6 diagonal cuts along parallel diagonals of opposite faces through a cube are objects with 4 distinct points with volume=0.
		

Crossrefs

Cf. A103157 binomial((n+1)^3, 4), A103656 triangular pyramids with volume>0 in lattice cube. a(n)=A103157(n)-2*A103656(n).