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Search: id:A099197
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| A099197 |
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Figurate numbers based on the 10-dimensional regular convex polytope called the 10-dimensional cross-polytope, or 10-dimensional hyperoctahedron, which is represented by the Schlaefli symbol {3, 3, 3, 3, 3, 3, 3, 3, 4}. It is the dual of the 10-dimensional hypercube. |
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+0
3
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| 0, 1, 20, 201, 1360, 7001, 29364, 104881, 329024, 927441, 2390004, 5707449, 12767184, 26986089, 54284244, 104535009, 193664256, 346615329, 601446996, 1014889769, 1669752016
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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H. S. M. Coxeter, Regular Polytopes, New York: Dover, 1973.
J. V. Post, "4-Dimensional Jonathan numbers: polytope numbers and Centered polytope numbers of Higher Than 3 Dimensions", Draft 1.5 of 9 a.m., 12 March 2004, circulated by e-mail.
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LINKS
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H. K. Kim, On Regular polytope numbers.
J. V. Post, Table of polytope numbers, Sorted, Through 1,000,000.
J. V. Post, Math Pages.
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FORMULA
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a(n) = 10-crosspolytope(n) = (n^2)*(2*n^8+120*n^6+1806*n^4+7180*n^2+5067)/14175.
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EXAMPLE
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a(5) = 7001 because 10-crosspolytope(5) = (5^2)*(2*5^8 + 120*5^6 + 1806*5^4 + 7180*5^2 + 5067)/14175 = 7001, but there is no a prioi way to expect that 10-crosspolytope(5) is prime.
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CROSSREFS
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Cf. A000332, A014820, A005900.
Sequence in context: A103261 A120796 A120787 this_sequence A041766 A121088 A133070
Adjacent sequences: A099194 A099195 A099196 this_sequence A099198 A099199 A099200
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 16 2004
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