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A099196
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Figurate numbers based on the 9-dimensional regular convex polytope called the 9-dimensional cross-polytope, or 9-dimensional hyperoctahedron, which is represented by the Schlaefli symbol {3, 3, 3, 3, 3, 3, 3, 4}. It is the dual of the 9-dimensional hypercube.
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4
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0, 1, 18, 163, 996, 4645, 17718, 57799, 166344, 432073, 1030490, 2286955, 4772780, 9446125, 17852030, 32398735, 56730512, 96220561, 158611106, 254831667, 400030580
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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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Table of n, a(n) for n=0..20.
H. K. Kim, "On Regular polytope numbers.
J. V. Post, Table of polytope numbers, Sorted, Through 1,000,000.
Index to sequences with linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
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FORMULA
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a(n) = 9-crosspolytope(n) = n*(2*n^8 + 84*n^6 + 798*n^4 + 1636*n^2 + 315)/2835.
G.f.: x*(1+x)^8/(1-x)^10. [Colin Barker, May 01 2012]
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EXAMPLE
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a(20) = 400030580 because 9-crosspolytope(20) = 20*(2*20^8 + 84*20^6 + 798*20^4 + 1636*20^2 + 315)/2835 = 400030580.
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CROSSREFS
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Cf. A000332, A014820, A005900.
Sequence in context: A158808 A128797 A008418 * A041618 A055915 A208827
Adjacent sequences: A099193 A099194 A099195 * A099197 A099198 A099199
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Nov 16 2004
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STATUS
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approved
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