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Search: id:A103656
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| A103656 |
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(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. |
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+0
5
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| 29, 7316, 285400, 4508716, 42071257, 273611708, 1379620392, 5723597124, 20398039209, 64302648044, 183316772048, 480140522044, 1170651602665
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OFFSET
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1,1
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COMMENT
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The observed growth rate of CPU time required to compute more terms is approximately ~ n^10.5.
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EXAMPLE
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a(1)=29: Only 58 of the A103157(1)=70 possible ways to chose 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.
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CROSSREFS
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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: A144233 A125074 A033519 this_sequence A028459 A127425 A135253
Adjacent sequences: A103653 A103654 A103655 this_sequence A103657 A103658 A103659
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KEYWORD
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hard,more,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Feb 14 2005
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