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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.
3
12, 2918, 64576, 673943, 4058656, 19462319, 70636336, 224091378, 621046332, 1573877652, 3582064304, 3582064304, 15781332296
OFFSET
1,1
EXAMPLE
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).
Sequence in context: A006272 A111237 A028666 * A271515 A231042 A370300
KEYWORD
hard,more,nonn
AUTHOR
Hugo Pfoertner, Feb 14 2005
STATUS
approved