A103656 a(n) = (1/2)*number of non-degenerate triangular pyramids that can be formed using 4 distinct points chosen from an (n+1) X (n+1) X (n+1) lattice cube.

29, 7316, 285400, 4508716, 42071257, 273611708, 1379620392, 5723597124, 20398039209, 64302648044, 183316772048, 480140522044, 1170651602665

Offset

1,1

Comments

The observed growth rate of CPU time required to compute more terms is approximately ~ n^10.5.

Links

Table of n, a(n) for n=1..13.

Example

a(1)=29: Only 58 of the A103157(1)=70 possible ways to choose 4 distinct points from the 8 vertices of a cube result in pyramids with volume > 0: 2 regular tetrahedra of volume=1/3 and 56 triangular pyramids of volume=1/6. The remaining A103658(1)=12 configurations result in objects with volume=0. Therefore a(1)=(1/2)*(A103157(1)-A103658(1))=58/2=29.

Crossrefs

Cf. A103157 binomial((n+1)^3, 4), A103158 tetrahedra in lattice cube, A103658 4-point objects with volume=0 in lattice cube, A103426 non-degenerate triangles in lattice cube.

Sequence in context: A267955 A267909 A265464 * A201489 A028459 A199369

Adjacent sequences: A103653 A103654 A103655 * A103657 A103658 A103659

Keyword

hard,more,nonn

Author

Hugo Pfoertner, Feb 14 2005

Status

approved