

A103656


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


4



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

1,1


COMMENTS

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


LINKS



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 4point objects with volume=0 in lattice cube, A103426 nondegenerate triangles in lattice cube.


KEYWORD

hard,more,nonn


AUTHOR



STATUS

approved



