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A099195
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Figurate numbers based on the 8-dimensional regular convex polytope called the 8-dimensional cross-polytope, or 8-dimensional hyperoctahedron, which is represented by the Schlaefli symbol {3, 3, 3, 3, 3, 3, 4}. It is the dual of the 8-dimensional hypercube.
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4
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0, 1, 16, 129, 704, 2945, 10128, 29953, 78592, 187137, 411280, 845185, 1640640, 3032705, 5373200, 9173505, 15158272, 24331777, 38058768, 58161793, 87037120
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| 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
| 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
| a(n) = 8-crosspolytope(n) = (n^2)*( n^6 + 28*n^4 + 154*n^2 + 132 )/315.
G.f.: x*(1+x)^7/(1-x)^9. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 18 2009]
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EXAMPLE
| a(10) = 411280 because 8-crosspolytope(10) = (10^2)*( 10^6 + 28*10^4 + 154*10^2 + 132 )/315 = 411280.
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CROSSREFS
| Cf. A000332, A014820, A005900.
Sequence in context: A067488 A120785 A031156 * A041486 A196642 A196595
Adjacent sequences: A099192 A099193 A099194 * A099196 A099197 A099198
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 16 2004
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